jeopardy directions for the game: 1. you will need a pencil and paper to keep score
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Jeopardy Directions for the game: 1. You will need a pencil and paper to keep score. 2. On the next screen, click ONCE on a question. 3. Read the Question and decide on your answer. 4. Click ONCE on the screen If you’re right, add your - PowerPoint PPT PresentationTRANSCRIPT
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© Mark E. Damon - All Rights Reserved
JeopardyDirections for the game:
1. You will need a pencil and paper to keep score. 2. On the next screen, click ONCE on a question. 3. Read the Question and decide on your answer. 4. Click ONCE on the screen If you’re right, add your
points to your total. If you are wrong, subtract those points.
5. Click ONCE on the button to go back to try another question.
6. Ready? Click ONCE to go the the Jeopardy board! 7. Press the “Esc” button on the keyboard to end the game.
Have fun!
Home
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Derivatives Limits Integrals
Applications Misc.
Other stuff
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Final Jeopardy
Scores
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Calculate the derivative of
ex
Calculate the derivative of
ex
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exex
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Calculate the derivative of
f(x) = x sin (x)
Calculate the derivative of
f(x) = x sin (x)
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f’(x) = x cos (x) + sin (x)f’(x) = x cos (x) + sin (x)
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Calculate the derivative of
Y = X2(X- 2)5
Calculate the derivative of
Y = X2(X- 2)5
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Home
y’ = 5x2(x-2)4 + (x-2)5(2x)
y’ = x(x-2)4(7x-4)
y’ = 5x2(x-2)4 + (x-2)5(2x)
y’ = x(x-2)4(7x-4)
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Use Implicit Differentiation to calculate y’
X2 + XY + Y3 = 3
Use Implicit Differentiation to calculate y’
X2 + XY + Y3 = 3
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2x + xy’ + y + 3y2 y’ = 0
y’ = -2x – y
X + 3y2
2x + xy’ + y + 3y2 y’ = 0
y’ = -2x – y
X + 3y2
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Find the derivative of the following function
F(x) = x3 – 3x2 + 4
x2
Find the derivative of the following function
F(x) = x3 – 3x2 + 4
x2
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y’ = x3-8
x3
y’ = x3-8
x3
Home
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Evaluate
Lim 6X - 3
Evaluate
Lim 6X - 3X → 4X → 4
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2121
Home
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Evaluate
Lim sin x
x
Evaluate
Lim sin x
xX → 0X → 0
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1 1
Home
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Evaluate
Lim l x – 4 l
x - 4
Evaluate
Lim l x – 4 l
x - 4X → 4X → 4
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No limitNo limit
Home
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Evaluate
Lim X2 – 9
X + 3
Evaluate
Lim X2 – 9
X + 3X → - 3X → - 3
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-6-6
Home
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Evaluate
Lim (X + ΔX)2 + 1 – (X2 + 1)
ΔX
Evaluate
Lim (X + ΔX)2 + 1 – (X2 + 1)
ΔXΔX → 0ΔX → 0
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(X+ΔX)^2 + 1 – X^1 -1 Δ X cancel 1’s
X^2 + 2XΔX + ΔX^2 – X^2 Δ X square and simplify
2X + Δ XΔ X = 0Answer = 2X.
(X+ΔX)^2 + 1 – X^1 -1 Δ X cancel 1’s
X^2 + 2XΔX + ΔX^2 – X^2 Δ X square and simplify
2X + Δ XΔ X = 0Answer = 2X.
Home
2X2X
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Evaluate
∫ 2x dx
Evaluate
∫ 2x dx
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x2 + cx2 + c
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Evaluate
∫ x3 + 2x
x
Evaluate
∫ x3 + 2x
x
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1/3 x3 +2x + c
(cancel one x and then integrate)
1/3 x3 +2x + c
(cancel one x and then integrate)Home
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Evaluate
∫ (lnx)3 dx
x
Evaluate
∫ (lnx)3 dx
x
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Let U = Lnx, du = 1/x dx
= ¼ (ln x)4 + c
Let U = Lnx, du = 1/x dx
= ¼ (ln x)4 + c
Home
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Evaluate
∫ cos 2x dx
Evaluate
∫ cos 2x dx
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½ sin(2x) + c½ sin(2x) + c
Home
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Evaluate
∫xe-x2 dx
Evaluate
∫xe-x2 dx
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Let u = -x2, du = -2x
-½ ∫ eu du
-½ e-x2+c
Let u = -x2, du = -2x
-½ ∫ eu du
-½ e-x2+c
Home
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In an application problem relevant to motion, the first
derivative of an equation tells ____________.
In an application problem relevant to motion, the first
derivative of an equation tells ____________.
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VelocityVelocity
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In an application problem relevant to motion, the second
derivative tells ______________.
In an application problem relevant to motion, the second
derivative tells ______________.
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AccelerationAcceleration
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A hot-air balloon is rising straight up from a level field and is being tracked by a range finder located
500ft from the balloon. At the moment the range finder’s angle of elevation is π/4, the angle is increasing at the rate of 0.14
rad/min. How fast is the balloon rising at that moment?
A hot-air balloon is rising straight up from a level field and is being tracked by a range finder located
500ft from the balloon. At the moment the range finder’s angle of elevation is π/4, the angle is increasing at the rate of 0.14
rad/min. How fast is the balloon rising at that moment?
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$300$300 Draw a picture
Θ = the angle the range finder makes with the ground
Y = the height of the balloon (in feet)
T = time, and θ and y are differentiable functions of t.
Y = 500 tan θ
Y’ = 500 (sec2θ)dθ/dt
Y’ = 500(2)(.14) = 140ft/min
Draw a picture
Θ = the angle the range finder makes with the ground
Y = the height of the balloon (in feet)
T = time, and θ and y are differentiable functions of t.
Y = 500 tan θ
Y’ = 500 (sec2θ)dθ/dt
Y’ = 500(2)(.14) = 140ft/minHome
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Air is being pumped into a spherical balloon to cause its
volume to increase at a rate of 100cm3/s. How fast is the radius of the balloon increasing when the
diameter is 50 cm?
Air is being pumped into a spherical balloon to cause its
volume to increase at a rate of 100cm3/s. How fast is the radius of the balloon increasing when the
diameter is 50 cm?
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1/(25π) cm/s1/(25π) cm/s
Home
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Car A is traveling west at 50 mi/h while car B is traveling north at 60 mi/h. Both cars are headed
towards intersection C. At what rate are the cars approaching
each other when car A is 0.3 mi from the intersection, and car B is 0.4 mi from the intersection?
Car A is traveling west at 50 mi/h while car B is traveling north at 60 mi/h. Both cars are headed
towards intersection C. At what rate are the cars approaching
each other when car A is 0.3 mi from the intersection, and car B is 0.4 mi from the intersection?
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- 78 mi/h- 78 mi/h
Home
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Find the derivative of
y = ln(x3 + 1)
Find the derivative of
y = ln(x3 + 1)
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y’ = 3x2
X3+ 1
y’ = 3x2
X3+ 1
Home
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Find the derivative of
y = 6(x2)
Find the derivative of
y = 6(x2)
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y’ = (ln 6)(6^x^2)(2x)y’ = (ln 6)(6^x^2)(2x)
Home
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Find the second derivative of
y = x3 + 3x2 – ½ x + 5
Find the second derivative of
y = x3 + 3x2 – ½ x + 5
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Home
y = x3 + 3x2 – ½ x + 5
y’ = 3x2 + 6x – ½
y” = 6x + 6
y = x3 + 3x2 – ½ x + 5
y’ = 3x2 + 6x – ½
y” = 6x + 6
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Find y’
y = ln [x(1+x)2]
Find y’
y = ln [x(1+x)2]
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y’ = lnx +2ln(1+x)
y’ = 1/x +2/(1+x)
y’ = lnx +2ln(1+x)
y’ = 1/x +2/(1+x)
Home
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A farmer has 2400 feet of fencing to create a rectangular pen for his
lamas next to their new barn. If the barn side off the pen does not
need a fence, what are the dimensions of the pen with the
largest area?
A farmer has 2400 feet of fencing to create a rectangular pen for his
lamas next to their new barn. If the barn side off the pen does not
need a fence, what are the dimensions of the pen with the
largest area?
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$500$500A = LW = xy
A = 2x + y = 2400
y = 2400 - 2x
A = x(2400 – 2x) = 2400x – 2x2
A’ = 2400 – 4x
X = 600 ft
Y = 1200 ft
A = LW = xy
A = 2x + y = 2400
y = 2400 - 2x
A = x(2400 – 2x) = 2400x – 2x2
A’ = 2400 – 4x
X = 600 ft
Y = 1200 ftHome
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List the antiderivatives for the following trig functions
Sin Cos Tan
List the antiderivatives for the following trig functions
Sin Cos Tan
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-cos, sin, sec2-cos, sin, sec2
Home
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Evaluate the integral
∫ (4 + 3x2) dx
Evaluate the integral
∫ (4 + 3x2) dxo
2
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1010
Home
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When is it good to use implicit differentiation?
When is it good to use implicit differentiation?
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When an equation can not be easily solved for y in terms of x.
When an equation can not be easily solved for y in terms of x.
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Complete the statement.
Lim [ f(x) + c(g(x))] =
Lim f(x) + ________________
Complete the statement.
Lim [ f(x) + c(g(x))] =
Lim f(x) + ________________x → a
x → a
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+ c Lim g(x)+ c Lim g(x)
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x → a
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In words, state the product rule and the quotient rule.
In words, state the product rule and the quotient rule.
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$500$500Product rule: first time the
derivative of the second + second time the derivative of the first.
Quotient rule: bottom time the derivative of the top – top times the derivative of the bottom all divided by the bottom squared.
Product rule: first time the derivative of the second + second
time the derivative of the first.
Quotient rule: bottom time the derivative of the top – top times the derivative of the bottom all divided by the bottom squared.
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CalculusCalculus
Final Jeopardy Question
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Calculate the derivative of
y = 2π4
Calculate the derivative of
y = 2π4
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y’ = 0y’ = 0
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