25,270 Answered Questions for the topic calculus

Calculus

01/22/24

The power (P) delivered to a load by a current of i amperes through a resistance of 9 ohms (when 110V are supplied at one end of the line) is given by the formula P= 110i -9i^2.

Determine the maximum power that can be delivered. Give your answer to four decimal places.
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Calculus

01/21/24

Consider the point (x, y) lying on the graph of the line
Consider the point (x, y) lying on the graph of the line 8x + 7y = 3. Let L be the distance from the point (x,y) to the origin (0,0). Write L as a function of x.
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Calculus

01/21/24

Use the following partial graph of a polynomial function, with a local maximum at x=-4 and a local minimum at x=2

Compare f(1.9) and f(2.1) with f(2)
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Calculus

01/21/24

Determine the extreme values of the function f(x)=x^2-8x+9, where -1≤x≤5. What is the absolute minimum and the absolute maximum?
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Calculus

01/21/24

Use the following partial graph of a polynomial function, with a local maximum at x=-4 and a local minimum at x=2

Compare f(1.9) and f(2.1) with f(2)
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Calculus

01/21/24

Give an example of a function for which f'(x)= 0 does not yield minimum or maximum.
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Calculus

01/21/24

Determine the extreme values of the function f(x)=x^2-8x+9, where -1≤x≤5. What is the absolute minimum and the absolute maximum?
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Calculus

01/21/24

User Use the following partial graph of a polynomial function, with a local maximum at x=-4 and a local minimum at x=2

Compare f(1.9) and f(2.1) with f(2)
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Calculus

01/21/24

determine the point of inflection, if it exists, on the graph of f(x)=5x^3+4x^(5/2)
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Calculus

01/21/24

Use the function f ( x ) = x^2 − 4 √ x to answer the following questions. a) where is the curve concave upward or downward. b) locate the point of inflection(if any) c) sketch the graph.
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Calculus

01/21/24

a rock is dropped from a high building. The acceleration due to gravity is -10m/s^2. Find the distance travelled by this rock from t=2s to t=4s
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Calculus

01/21/24

Find the mean value of the function f(x)=3x^2-x over the interval x=1 to x=2
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Calculus

01/21/24

the acceleration a (in cm/s^2) at time t (in seconds) of a vibrating wire is given by a= -0.01 (1024pi)^2 cos1024πt.

Determine the velocity v and position s at any time, if s=0.01 cm and v=0 cm/s at t=0s.
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Calculus

01/21/24

Sketch the region in the first quadrant enclosed by the curves given below.

y=arccos(x/2)y=(pi/4)(2-x)Decide whether to integrate with respect to x or y. Then find the area of the region. In my previous unsuccesful attempts I have gotten -pi/2 and 4-pi. But they are all... more
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Calculus

01/20/24

Find the total area enclosed by y=x^3-4x and the x-axis, between the vertical lines x=-2 and x=3 draw a diagram to illustrate your solution.

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01/20/24

Electricity and Magnetism question. Please help ASAP!
A uniformly charged insulating rod of length 17.0 cm is bent into the shape of a semicircle as shown in the figure below. The rod has a total charge of −7.50 µC. The link to the figure is... more
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Calculus

01/20/24

Consider the region bounded above by f(x) =x, below by the x-axis, on the left by x= 0,and on the right by x= 5. The region has been divided into five vertical strips.

Write the definite integral representing the exact area, and evaluate that integral
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Calculus

01/20/24

if y'0 and y=1 when x=2 and y''-4=0, find the function
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Calculus

01/19/24

can this only be evaluated to 0/8 or is there a way to algebraically manipulate it?
Lim (x2-4)/(x2+4)x->2can this only be evaluated to 0/8 or is there a way to algebraically manipulate it?
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Calculus

01/19/24

How large should n be to guarantee that the Simpson's Rule approximation to

integral 0 to 1 e^(x^2) dx is accurate to within 0.00001?I got f''''(x)=(16x^4+48x^2+12)e^(x^2) and now I have to show how to evaluate |(16x^4+48x^2+12)e^(x^2)|<=kPlease help me how to evaluate... more
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Calculus

01/19/24

Evaluate the integral
∫sinx*ecos(x)
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Calculus

01/19/24

Evaluate the integral
∫(3x)/(x2+6)dxI used u-substitution for the first part, u=x2+6, du=2xdx, 1/2du=xdxI put the substitutions back into the equation and took out the constant from the integral, getting 3/2∫1/udu (3/2... more
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Calculus

01/19/24

Differentiate the following functions. You do not need to simplify.
First question: f(x)=tan(lnx)+ln(5x3/2-1)For the first part, I got 1/x(sec2(lnx)) by doing the chain rule. The derivative of tan is sec2(x) and the derivative of ln(x) was 1/x, but I'm not sure how... more
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Calculus

01/18/24

A manufacturer needs to design an open box having a square base, and a total exterior surface area of 75 square inches. What dimensions will provide the largest possible volume?
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Calculus Math

01/18/24

How many critical points: cosine function
The derivative of a function g is given by,g'(x) = cos((x-pi/2)x)How many critical points does the function have on the interval [1.8, 3.7]?A. 0B. 3C. 5D. 6
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