25,270 Answered Questions for the topic calculus

Calculus

08/02/23

Find F ' (x) given that
F(x)= (2x3+3x2-5)(5x2-2x+1)
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Calculus

08/02/23

Find f ' (x) given that
x2+5xF(x)= ‾‾‾‾‾‾‾‾‾‾ 3x3+4
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Calculus

08/02/23

Sketch the graph of the floor function
f(x) =[x + 1] , over the interval [-3, 3)
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Calculus

08/02/23

Sketch the graph of a function f having the given characteristics.
f(1) = f(3) = 0f ′(x)<0 for x < 2f ′(2) does not exist f′(x)>0 for x > 2f ″(x) < 0,   x ≠ 2
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Calculus

08/01/23

Let region R be the shaded region in the first quadrant enclosed by the graphs of y=sinx y=cosx, and the y axis
find the area of region R, find the volume of the solid generated when R is revolved around the x and y axis
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Calculus

08/01/23

How can I find the Estimate the value(s) of c that satisfy the conclusion of the Mean Value Theorem on the interval [2, 6].

The question presents only the graph and since I don't know the equation, I don't know how to estimate it. information of the graphg is differentiable on the open interval (0, 8)g is continuous on... more
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Calculus

08/01/23

Find all relative extrema of the function f(x)= x^4 - 4x^2 + 2 by using the Second Derivative Test where applicable.
Find all relative extrema of the function f(x) = x4 - 4x2+ 2 by using the Second Derivative Test where applicable.
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Calculus

08/01/23

Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values c in the open interval (a, b) such that
f(b)-f(a)f'(c)= ‾‾‾‾‾‾‾‾‾‾‾ b-aIf the Mean Value Theorem cannot be applied, explain why not. x f(x) =‾‾‾‾‾‾ , [1, 4] x-5
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Calculus

08/01/23

Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
3x3=y 6, point (1, 2)
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Calculus

08/01/23

Can you help me solve this calculus question
Estimate the area under the graph of f(x) = 1/(x+3) over the interval over the interval [-2, 1] using eight approximating rectangles and right endpoints. Rn= Ln=
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Calculus

07/31/23

Find the second derivative of the function.

F(X) = 5(2-7x)4
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Calculus

07/31/23

Use the quotient rule to find the derivative of the function.
3t2-1 g(t)= ¯¯¯¯¯¯¯¯¯¯ 2t+5
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Calculus

07/31/23

Use the alternate form of the derivative to find the derivative at x=c, if it exists.
F(x)=x3+2x2+1, c=-2
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Calculus

07/31/23

the region in the first quadrant bounded on the left by the circle x^2+y^2=3 on the right by the line x=sqrt3 and above by the line y=sqrt3, about the y axis
find the volume of the solid
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Calculus

07/30/23

How many critical numbers does f have?

A formula for the derivative of a function f is given. How many critical numbers does f have? f'(x)= 100cos^2(x) / 10+x^2 -1 I know that the critical point exists where f'(x) does not exist and the... more
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Calculus

07/30/23

Let f(x)=x^3+6x^2+19x-1148.
A solution to f(x)=0 can be found between x=8 and x=9.The line tangent to the graph of y=f(x) at x=8 will have equation y=  An approximate solution to f(x)=0 can be found at x1=   .The line... more
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Calculus

07/30/23

Let f(x)=x^3-3x^2+20x-268
A solution to f(x)=0 can be found in the interval <x<(Enter a pair of consecutive integers m, M where a solution is guaranteed to exist in the interval m<x<M).If you draw the line... more
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Calculus

07/30/23

Use Newton's method to approximate a root of the equation:
4x^3+8x+1=0 as follows.Let x1=-1 be the initial approximation.The second approximation x2 is:  and the third approximation x3 is:  
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Calculus

07/30/23

How fast (in knots) is the distance between the ships changing at 3 PM?

At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 18 knots. (Note: 1 knot is a speed of 1 nautical mile per hour.)
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Calculus

07/29/23

explicit derivative

2/x - 1/y = 4How can I solve the equation explicitly for y and differentiate to get y' in terms of x?
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Calculus

07/29/23

intersection vectors problem
Find the intersection of xyz=[1,4,−2]+t[1,−1,3] and 2x−5y+8z−28=0.
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Calculus

07/29/23

projection vectors problem
Given p→=[−1,4,−8 ]and q→=[10,10−9], find: 2p+5q→  p•q→  q×p→  p×q→  The angle between p→ and q→  projq→p→
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Calculus

07/29/23

proj vectors problem
Given a→=[2,−10 ]and b→=[−8,23] find: 3a−2b→  a•b→  a+b→  projb→a→ The angle between a→ and b→
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Calculus

07/29/23

vectors problems
Use geometric addition of vectors to find the resultant of each combination. 18 km/h north and 16 km/h east.  12 N on a bearing of 25° and 17 N on a bearing of 100°.  Determine the vertical and... more
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Calculus

07/29/23

pilot vectors problem
A pilot flies at 300 km/h with a heading of 110°. A 30 km/h wind comes from 250°. Find the bearing and speed of the plane’s resultant travel.
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