Find the indefinite below using the substitution x = tan (8). x √ √1² dx, for −1

Q: (cos-1+tan-¹) exactly (no calculators). 2 Evaluate sin (cos

A: We use  sin(A+B)=sin(x)cos(y)+cos(x)sin(y)

Q: A graph is defined by the equation y²(2-x) = x³. Part A: Find dy Part B: Find the equation of the…

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Q: 80. A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax³ + bx² + cx +…

A: f(x) = ax3+bx2+ cx + d on differentiating,   f '(x) = 3ax2 + 2bx +c which is a quadratic in x and…

Q: By the alternating series test, the series converges. Find its sum. First find the partial fraction…

A: The objective is to find the sum of the series.

Q: Find the second derivative. 6 Select one: A. 36 LIE

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Q: D and E

A: Note: Since the student has mentioned to solve only parts (d) and (e), so we are solving this…

Q: An open rectangular box (no top) is formed with a square base and rectangular sides so that the…

A: Solution is given below:

Q: -14T +7-4x 2. (a) Evaluate lim (b) Determine the equation of the vertical asymptote of f(x) = -14x

A: 2a)

Q: An open-top box is to be made from a 18-inch by 30-inch piece of plastic by removing a square from…

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Q: 8.) f(x) = (x+3)(x-4) 2(x-1)(x+2)

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Q: Let u(x) = sin(x) and v(x) = x20 and f(x): u'(x) = v'(x) = f' = u'v - uv' v² = u(x) v(x)

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Q: Compute the x(1)and x(4) for the function x(t) that satisfies the initial problem x"(t) + 2x(t) +…

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Q: A bank features a savings account that has an annual percentage rate of r 3.3% with interest =…

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Q: Let f(x) e = e-7x² Find F"(x). f"(x) = Find the x-value(s) where f"(x) = 0. (Enter your answers as a…

A: Topic = Derivative

Q: Find the total differential. w =

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Q: 4. At what point does the exponential function overtake the linear function on the interval (0,00)?…

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Q: Does the graph of the function below have any horizontal tangents in the interval 0≤x≤2x? If so,…

A: To determine whether the function below have any horizontal tangents in the interval 0≤x⩽2π. If so,…

Q: 1. Consider the iterated integral (a) Sketch the domain of integration. (b) Change the order of…

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Q: Which statement regarding these polynomials and their zeros is true? - ○f(x) = (x² − 1) (x + a) has…

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Q: Using Limits, find the instantaneous rate of change of the following function: f(x) = 2x^2 - 16x +…

A: Topic - Instantaneous rate of range of function using limits We are given,…

Q: Find the derivative of the function y = -7-5x. dx =

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Q: If log5 (log₂ (log3 x)) = 0 then x equals O (A) 0 O (B) 9 O (C) 5 O (D) none of the other answers is…

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Q: " x² cos(3x) dx find u, v and then find the answer.

A: Given query is to  find the integral.

Q: 8:49 A particle moves along the x-axis position at time 0 < t < 18 is g x(t), whose graph is shown…

A: We have to find the interval  such that particle is decreasing

Q: (2x+3) y'=y+ (2x+3) when x = -1, y = 0 . y'-(3 tanx)y = / 11/2

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: h(x)=-ln(x+2)

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Q: Find the present value of an ordinary annuity with deposits of $15,125 semiannually for 6 years at…

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Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 25. Answer =…

A: Given data÷ ∫∫Dx2+y23/2dxdy Where D is the disk x2+y2≤25   Now main part of conversion from…

Q: k=0 4(-2) is an alternating geometric series, which diverges. converges Σ 4( - 2)² k=0 Enter DNE for…

A: ∑k=0∞ 4-2k

Q: The plane y + z = 2 intersects the cylinder x2 + y2 = 5 in an ellipse. Find parametric equations for…

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Q: 4. Find all local maximums and local minimums for f(x) = x³ - 2x² + x - 1.

A: We have given function fx=x3-2x2+x-1 Derivative of the function is given as f'x=ddxfx…

Q: A waste management company is designing a rectangular construction dumpster that will be twice as…

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Q: 1. Find the length of the curve y = ln(secx), where 0 ≤ x ≤ (1.5 Marks)

A: Note: For a function f(x) and x=a to x=bthen arc length is given by ∫ab1+(f'(x))2dx. Now in the…

Q: x² e2x dx find u, v and then find the answer. S ومح

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Q: If x² + y² = 100 and dy/dt = 4, find dx/dt when y = 6. (Enter your answers as a comma-separated…

A: Topic = Derivative

Q: 4. If y = tan-¹(cos x), then dy = dx

A: As we know the Chain rule: fgx'=f'gx·g'x And Use the common derivatives.…

Q: Suppose that the radius r and volume V = πr3 of a sphere are differentiable functions of t. Write an…

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Q: Choose the correct statement about the below function 00 B O One to one and onto O One to one but…

A: By using function theory

Q: 2. (x2) y = y+2(x2)

A: Topic = Differential equation

Q: At 6 P.M. an oil tanker traveling west in the ocean at 18 kilometers per hour passes the same spot…

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Q: 1. f(x)= sqrt(x^2-4) Where is the function positive? A) [0, infinity) B) (2,infinity) C) (0,…

A: 1) Given: sqrt(x2 - 4) we know that square root is not defined for negative input as we will get the…

Q: Sketch a graph of a function that is negative on(0,2), increasing on [2,4], and has x-intercepts at…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Directions: Circle each function that is an example of exponential decay (there are exactly five of…

A: As per the instruction, we will be answering the first three subparts. For (a), Graph: For (b),…

Q: 2. Evaluate the integrals 1 zx+z a) b) c) 6xzdydxdz 000 3 1 √1-z² SSS zey dxdzdy 000 1 2x y [ […

A: To find:- ∫01∫0z∫0x+z6xzdydxdz ∫03∫01∫01-z2zeydxdzdy ∫01∫x2x∫0y2yxzdzdydx

Q: What is the derivative of h(t) = 5/t + 6/t^2?

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Q: Find the point on the line 4x+3y−4=0 which is closest to the point (2,−3)

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Q: a) Sketch a graph for the polynomial function. You must include all key features of polynomial…

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Q: An island is 6 mi from the nearest point on a straight shoreline; that point is 12 mi from a power…

A: Concept: The slope of a function can be found in its first derivative. The slope of the curve grows…

Q: 3-8 Test the series for convergence or divergence. dhe tadt Hour 3.- + - + 1

A: 3. The given series is 47-48+49-410+411-....... We have to find the series is convergence or…

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 7…

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