16,633 Answered Questions for the topic calculus

Calculus

10h

#### Evaluate the following limits. If needed, enter oo for ∞ and -oo for − ∞ .

(a)limx→∞3+7x/4−6x= (b)limx→−∞3+7x/4−6x=

Calculus

11h

#### Consider the function f ( x ) = 5 x 3 − 5 x on the interval [ − 2 , 2 ] . Find the average or mean slope of the function on this interval.

Consider the function f(x)=5x3−5x on the interval [−2,2]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one c in the...
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Calculus

11h

#### For the above quartic polynomial f( x ) = − x 4/ 2 − x 3 + 6 x 2 , identify the interval on which f is concave up. < x <

For the above quartic polynomial f( x ) = −x4/2−x3+6x2, identify the interval on which f is concave up. < x <

Calculus

12h

#### f ( x ) = 2 x 3 − 42 x 2 + 240 x + 11

The function f(x)=2x3−42x2+240x+11 has one local minimum and one local maximum.This function has a local minimum at x equals with value and a local maximum at x equals with value

12h

#### How do I express the answer graphically and algebraically?

A motorcycle stunt rider jumped over the canyon. The path of her motorcycle was given approximately by the function H(x)=−0.005x^2+4.2x+900, where H is measured in feet above the ground and x is...
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Calculus

14h

#### Related Rates Calculus

The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 2cm/s. When the length is 30cm and the width is15cm how fast is the area of the rectangle...
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Calculus

14h

#### Related Rates Calculus

A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is the rate is the volume of the snowball changing when the diameter is 8 cm? The volume is...
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Calculus

14h

#### Related Rates Calculus

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How...
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Calculus

14h

#### Related Rates Calculus

When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV 1.4 = C where C is a constant. Suppose that at a certain instant the...
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Calculus

14h

#### Related Rates Calculus

If the radius of a sphere is increasing at a constant rate of 3cm/sec , then the volume is increasing at a rate of __________ cm3/sec when the radius is 5cm. Hint: dV/dt = dV/dr * dr/dt , and the...
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Calculus

14h

#### Related Rates Calculus

Let A be the area of a circle with radius r. If dr/dt = 2, find dA/dt when r = 3Answer:

Calculus

16h

#### calculus math 202

Given 2x2y - 2y3 = 5x - 4 , use implicit differentiation to find the derivative y'=dy/dx and evaluate it at the point (x,y)=(2,1).
a
y' = 9/25
b
y' = -9/7
c
y' = 4/3
d
y' = -3/4
e
y'...
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Calculus

16h

#### calculus math 202

The area A of a disk of radius r is given by the formula A= πr2. Assume that the area increases at a rate of 3ft2/sec. Find the rate with which the radius increases at the moment when the diameter...
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Calculus

16h

#### calculus math202

Find the second derivative of f(x) = 5x ln(x) and evaluate it at x=2. (Enter your answer correct to at least three decimal places.)

Calculus

16h

#### Use the Concavity Theorem to determine where the given function is concave up and where it is concave down. Also find all inflection points.

f(x) = x 2 - 20x + 109
a
Concave down for all x; no inflection points
b
Concave up for all x; no inflection points
c
Concave up on (10, ∞), concave down on (-∞, 10); inflection point (10,...
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Calculus

22h

#### Tangents and Intersection

Tangents and Intersection. Find the two tangent slopes (exact values) at the point where the graph of the equation y^x = x^y intersects the graph of y = log base 2 (x) Include your computations of...
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Calculus

22h

#### A Projectile. When a projectile is launched upward from the top of a building of height H, its vertical position (in feet) at time t (in seconds) is given by

A Projectile. When a projectile is launched upward from the top of a building of height H, its vertical position (in feet) at time t (in seconds) is given by. Show Works = -16t^2 + 96t +Ha) Find...
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Calculus

1d

#### What's the volume?

Use the Shell Method to find the volume of a solid obtained by rotating the region B about the x-axis.y = x^2 + ba = 4, b = 5volume= ?

Calculus

1d

#### Walk me through the question in the description or at least get me started.

Let f: R -> R be the function defined by the piece-wise function: {cos (pi x), if x < – 2f(x) = { ax + b , if –2 <= x <= 2, and { x³ , if x > 2where a and b are...
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Calculus Math

1d

#### A function is given. h(t) = t^2 + 5t; t = −1, t = 3

Determine the average rate of change of the function between the given values of the variable.

1d

#### (x)=√(5x+10), find f′(x) using the definition f′(x)= lim, h→0, {f(x+h)−f(x)} / h . Then, using this, find the tangent line to the graph of y= √(5x+10) at x=3. Enter

For f(x)=√(5x+10), find f′(x) using the definition f′(x)= lim, h→0, {f(x+h)−f(x)} / h . Then, using this, find the tangent line to the graph of y= √(5x+10) at x=3. Enter all values as integers, or...
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