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... more
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... more
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... more
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... more
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... more
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... more
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... more
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'... more
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... more
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,... more
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... more
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... more
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

(arcsec x) ^ tan x = y

(sec-1 x)tan x = yFind dy/dx.

1d

Identify where any horizontal tangents exist for the function:

𝑓(𝑥)=𝑥3+7𝑥2−8
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... more
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.

(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... more

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