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Calculus

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Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx

Q: Find the limit L. Then use the - definition to prove that the limit is L

A: Consider the given limit:

Q: Sums and dierences In the accompanying figure, it looks as if v1 + v2 and v1 - v2 are orthogonal. I...

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Q: Trigonometric integrals Evaluate the following integrals. ∫sin2 3x dx

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Q: Is the following function a valid probability density function? 3x² – if - 1<x< 1, f(x) = otherwise....

A: 1. f(x) ≥ 0 for all x

Q: Use an identity to solve the equation sin (x + π/4) + sin (x - π/4) = 1 on the interval [0, 2π).

A: We will use sin(A+B)=sinAcosB+cosAsinB and sin(A-B)=sinAcosB-cosAsinB

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (I...

A: Consider the given function: Here the objective is to find the interval in which f(x) is increasing...

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate,of the conic sections x2 + 2...

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Q: he 3x3 matrix A siven below. 1 2 A - 1 2. the determinont of A (Do not Sarrus n Use

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Q: Calculate the derivative d dæ In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: First, we split the integral function into two terms. Now find the derivative of both integrals by ...

Q: Describe the type of indeterminate form (if any) that is obtained by direct substitution. (a) Evalua...

A: We try to find the limit by substitution first

Q: Let A be a nonsingular k x k matrix with k> 1. Show that. det [adj(A)] = [det(A)]*-1

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Q: Explain how to find the least common denominator for denominators of x2 - 100 and x2 - 20x + 100 ?

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Q: Absolute maxima and minima Determine the location and value of the absolute extreme value of ƒ on th...

A: Given

Q: The following functions are positive and negative on the given interval.a. Sketch the function on th...

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Q: College students are graduating with the highest debt burden in history. The bar graph shows the mea...

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Q: find the line integrals along the given path C. ∫C (x - y) dx, where C: x = t, y = 2t + 1, for 0≤ t≤...

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Q: Minimum-surface-area box Of all boxes with a square baseand a volume of 8 m3, which one has the mini...

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Q: Below is the graph of y = z2 +5. 301 2어 1어 -4 -3 -2 -1 0 i 2 3 4 5 The area bounded by y = z2 +5 and...

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Q: Find cos 0 if cot 0 =4/3 and sin 0 < 0.

A: Also given that sinθ<0, this means sinθ is negative. So, cotθ=cosθ/sinθ means cosθ also have to b...

Q: A large koi pond is filled from a garden hose at the rate of 10 gal/min. Initially, the pond contain...

A: a) Given that initially, there was 300 gal of water. And water is entering at a rate of 10 gal/min....

Q: Find the limits

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Q: Evaluating integrals Evaluate the following integral.

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Q: Let P(x, y) be a point on the graph of y = x2 - 8. Express the distance, d, from P to the origin as ...

A: To find the distance from point P (x, y) to the origin (0, 0).

Q: Evaluate ∫tan4 x dx.

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Q: Computing flux Use the Divergence Theorem to compute thenet outward flux of the following fields acr...

A: Given Sphere S:

Q: Consider the following. Find the indefinite integral and set up the limit that will be used to e...

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Q: For y = Cekt, explain why exponential growth occurs when k > 0 and exponential decay occurs when ...

A: For y = Cekt, explain why exponential growth occurs when k > 0 and exponential decay occurs when ...

Q: Find the derivative of h(x) = (3x − 2x2)(5 + 4x)

A: We first expand h(x)

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 + z2...

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the fun...

Q: Calculus Question

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 4 + (I...

A: Given

Q: (b) Solve the following ordinary differential equation using Runge-Kutta classical method. Compute u...

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Q: Find g(1).

A: (Because the upper and the lower limits are same, so the integral is 0)

Q: the graph of ƒ' is given. Assume that ƒ iscontinuous, and determine the x-values corresponding to lo...

A: Local maximum occurs if f(x) goes from increasing to decreasing. That means f'(x) goes from positive...

Q: Determine an equation for the tangent line to f-(x) at (4, 7) given that y-4= (x - 7) is an equation...

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