4 x² + 4x - 5 Consider using Trigonometric Substitution find x . x +2 sec e O 3 sec e O -2+ sec e O -2 +3 sec 0

Q: If t = x + ex, find d2x/dt2 given dx/dt = 1 / 1+ex.

A: dcdt=0 , where , 'c' is any constant. dexdt=ex .dxdt

Q: 4" converges or diverges. (7n)2 Use the ratio test to determine whether n=6 (a) Find the ratio of…

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Q: Evaluate the following integrals: (a) / dx V2x2+1 (b) / sin(In(x)) dx (c) S(x² + 2x)e2* dx

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Q: Suppose a sample of a certain substance decayed to 77.2% of its original amount after 300 days.…

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Q: 15х2—х3— 43х — 19 Ax + B C The integral /- D + rx +s -dx can be rewritten as dx. (x+1)2(x²– 6x + 13)…

A: The integral ∫15x2-x3-43x-19x+12x2-6x+13 dx can be written as ∫Ax+Bax2+bx+c+Cmx+nt+Drx+s dx.To…

Q: we the system. If the system has one unique solution, write the solution set. Otherwise, determine…

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Q: completing the square, show that r1/2 da 2² – r+1 3/3

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Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x? + xy + y? - 9x…

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Q: Consider the initial value problem y'(t) = t² - 3y, y(3) = 1. What is the approximation to y(3.1)…

A: Here we have to use the Euler's method.

Q: 12. Find dy/dx (x – 2)(x + 1) 3 X y = (х — 3)4 -

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Q: Find two unit vectors orthogonal to a = (-5, 2,2) and b = (5, 4, -2) Enter your answer so that the…

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Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: a Derivative In Exercises 59-84, find the Finding derivative of the function. 60. y = (x² – 6)3

A: Topic = Derivative

Q: 3. Let h(x) be a twice-differentiable function with h' (x) <0 and h" (x) <0 for all real numbers x,…

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Q: 3x²+ 7x+28 A f (x) Using Partial Fractions in evaluating -dx, the decomposed fraction is - x3+x²+7x…

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Q: The radius r of a sphere is increasing at a rate of 2 inches per minute. (a) Find the rate of change…

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Q: Question 8 If limx→a J(X): |8(x) lim;-»a [f(x)] = = 1 and limx→a g(x) : = o then, we must have %3D…

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Q: Reduction of order can be used with y = 3x to find a second solution for the DE: xy" + 2xy' + 2y =…

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Q: 5xy = 4x²z – 3yz2; yx and y,. -

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Q: The graph of a function f is given. (Let a = 1.) 0 1 8. (a) Estimate f(x) dx using four subintervals…

A: We have to estimate the given integral.

Q: 14. Find the third order Taylor polynomial T3(x) of the given function at the given point. (a) S(1)…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: dx J Evaluate: (x-4)(x-1) A None of the given choices 1 B x-1 +C X-4 (c) x-1 3ln X-4 + C 1 D X-4 + C…

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Q: Let A = (1, -2) and B = (6, 2). Solve for projyA. %3D

A: projBA  implies projection of A on the vector B. projBA =A·BB2 B  ............(1) A·B is dot product…

Q: ul = 7,0 = 25

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. S tan*, dr 2

A: (2). Given: I=∫tan4r2dr   ....(1)   As we know from the trigonometric identity; sec2x=tan2x+1 The…

Q: Learning activity: Plot the points (x,y) and draw a smooth curve defined by the parametric equation:…

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Q: B. f is not continuous at x =a C. f has a relative maximum at x = a D. f is continuous but not…

A: Here, we have given a function now we have to calculate the points where the function has point of…

Q: Consider the following piecewise function Quiz Content x² – 1 x 1 x2 Find the value(s) of a for…

A: Use the definition of  continuous function .

Q: 9-x2 dx. - х x2

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Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

Q: 3. Find the area bounded by the given curves. Rubrics: Curve accurately drawn with intercepts…

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Q: 3) Convert the following polar equations to rectangular equations. 1 a) r = b. r=4 4 cos 0-3 sin 0

A: (a)r=14cosθ-3sinθSince, x=r cosθ , y=r sinθso,cosθ=xr , sinθ=yrsubstitute in the given polar…

Q: Evaluate the integral. 28) 335 B)- 215 A) 325 D) 36

A: Given:      ∫05  3x2 + x +6 dx

Q: X Sin(x?)dx evaluate the definite integral

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Q: S sin°x cos³x dx 1 2 1 sin'x +sin°x - sin'"x + C sin'a +sin'x +sin"x +c B 1 sin'

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Q: Sveluate esing Sub method 7.

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim +00\ 5t2 + 6' 6t (?, ?)…

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Q: Determine whether the following series converges. Justify your answer. 00 3k° +k Σ 2k° - 2 k = 1

A: To determine whether the given series is convergent .

Q: S° g(t) dt

A: From the figure, we know the following. ∫010g(t)dt=Area of the semi circle - Area of the triangle…

Q: = sin? (esint) l(x) = tanh-1 x + In v1- x2 2 h(t) + cos + cos¯ -1(2t3 - 5) |

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Q: For the integral, / tan'x sec*x dx, if we let u = tan x, what is the re-written form of the…

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Q: 1 In solving the antiderivative of f(x) = 2 - sin(x) by miscellaneous substitution, the substitution…

A: Here we have to use the subsitution.

Q: If f(x) = Vx+3 and g(x) find g(f(x)). Answer 8(f(x)) =

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Q: Sketch and determine the center, foci and vertices of th equation of x2 (y-4)2 + 36 = 1. 49

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Q: Use a graphing utility to graph the function and find the absolute extrema of the function on the…

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Q: x2 In solving for the antiderivative of f(x) = [4-x² using trigonometric substitution, Jf(x)dx is…

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Q: Work problem 2 " ) You must provide clear and detailed solutions for each of the following…

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Q: 13. Find dy/dx of y = xnx

A: According to Bartleby's guidelines we can solve only 1 question at a time. Here's the solution of…

Q: Find the area between the curve and the x-axis over the indicated interval. 7 y =; [1, 6] ... The…

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Q: 2 2 y 6 L72 L48 yzdxdzdy =

A: Topic = Integration