1. For the right triangle pictured below, find the exact values of each of the following (no decimals or approximations, please): (a) cos(0) 4 (b) tan(0) (c) csc(0) 3

Q: Verify that the given functions are linearly independent by evaluating the Wronskian at x = 0. {e2a…

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Q: a3z a3z 5. For z = x?siny show that дудхду ay²əx

A: As per our norms we have to write one question at a time kindly repost remaining questions.

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Q: Find the one-slided limit (If it exists). (If the limit does not exist, enter DNE.) -6 lim x-4 (x-…

A: Given limx→4- -6(x-4)2 Apply the constant multiple rule limx→4- c f(x) = c limx→4-f(x) with c=-6…

Q: Part B. Find the equation of the circle of curvature of the curve y = 2x* – x at its minimum point…

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Q: Find the most general antiderivative. 4) (15+ e2t) dt. 16 e2t A) B)+ 202t + C e3t +C +C 27 e2t +C

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Q: 1-2 For each of the following functions given by power series, find f'(x) and / f(x) dx. Do not find…

A: To differentiate and integrate the given power series.

Q: Find the particular solution to the differential equation d?y = 4e* + 3x² dx2 dy given y = -3 and dx…

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Q: Find the Rlemann sum for f(x) = x +3x over the Interval [0, 8] (see figure), where %3D X, = 0, x, =…

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Q: by the ea vation 2xy +X=Y". XP |3D

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Q: (26) Let f(x) = x?e=*. For what value(s) of r does f(x) have a horizontal tangent?

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Q: Determine whether the SERIES converges or diverges. If it converges, find its SUM: n+2 n%3D2 A. It…

A: We have to find sum

Q: ri rV1-x² dy dx -1 Jo

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Q: ( 19 ' Evaluating cot 3 will yield to A 3 B -V3 D

A: Here, cot19π3cot6π+π3

Q: Y Evaluate the following integrals: 1) tan(3x +5) dx evs -1 2) dx 3) [Vx² -x' dx 4) sin(tan 0) sec 0…

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Q: 7. Determine the value(s) of x where the slope of the tangent line is horizontal. Use exact values.

A: If slope of the tangent line is horizontal ,set dydx=0.

Q: dy Use implicit differentiation to find for y' dx +2xy – x' = cos3y

A: Given:         y3+2xy-x5=cos3y Implicit differentiation:    differentiating on both sides with…

Q: (d) = 9- X-y = 2 at p(3,1), find x-2y dy 19we 1997109 oilt 00d:O dx dy (a) 으= 0 (b) = -1 (c) = 1 (=-…

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Q: Which equations parameterize the line from (3, 0) to (-2,-5) so that the line is at (3, 0) at t = 0,…

A: We know that the parametric equations of the line from x0, y0 to x1, y1 are given by xt = x0 + x1-x0…

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Q: Supply the missing integrand and the limits of integration sinx dy dx _dx| 1– y² dx (x=1) dx

A: This question can be solved using the concept of double integration.

Q: Find length of the curve described by the parametric equations a = 3t2, y = 2t, 0<t< V3. A. 3/3-1 B.…

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Q: - The price-supply and price-demand equations of a certain product are given by p = S(x) = 15+ 0.1x…

A: To find the producer surplus.

Q: Question Ris the region bounded by the functions f(x) = /3x - 1 and %3D g(x) = +2. Find the area A…

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Q: x³ + x² - x - 1 lim X→1 X-1

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Q: 8. Find the first four terms of the binomial series for Vx +1 .

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: 2. Find the volume of solid generated by revolving the area bounded by x=y2+2, x=0 and y=2 sbout: a)…

A: Given problem:- Find the volume of solid generated by revolving the area bounded by x = y2 + 2 , x =…

Q: 1+エ da. -dx. Evaluate the integral:

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Q: 1+sin (n) 2. Determine whether the series is convergent explain why. Ln=1

A: We have to test the series

Q: 9) y = e4x² + x A) dy dx 8xe2x + 1 B) dy - 8xex2 dx %3D + 1 C) dy dy - 8xe4x2 dx — 8хе + 1 %D D) + 1

A: We have to find

Q: Find the critical points of the function x -8x2 О 0,2, -2 O 0, 1 О 1,2, 3 this function does not…

A: Solution: Let f(x) = x4 - 8x2 find where f'(x) is equal to zero or undefined  f'(x) = 4x3 - 16x

Q: lim (1+ X00

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Q: 7) Assume that the temperature of a person during an illness is given by: T(t) = t2 +1 5t + 98.6, in…

A: topic - derivative of a function

Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f (x) = L X→a

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Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: Find the differential dy of the glven function. (Use "dx" for dx.) y = 3Vx + dy = Submit Answer

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Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

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Q: 0 1 7) [ [ysin x dxdy -1 -y

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Q: Evaluate the limit, using L'Hôpital's Rule If necessary. (If you need to use m or-m, enter INFINITY…

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Q: Question 3. Find f/(x). If f(x) = tan-1x?

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Q: (31) Use Newton's Method to make the second approximation r2 to the solution of 2e = ex. Take x1 =…

A: Leibnitz Rule of differentiation: ddx∫α(x)β(x) f(x,t) dt  = ∫α(x)β(x) d(f(x,t))dx dt +dβxdx f(x,βx)…

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A: Option (A)  4th Quadrant

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hoptal's Rule. 3(x-7) Iim x…

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Q: SOLVE THE FOLLOWING PROBLEMS SHOWING EVERY DETAIL

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Q: lim, -r(csc Tx )(Inx)] -TC

A: The given limit,limx→1-πcscπxln x

Q: ... Supply the missing integrand and the limits of integration -2 csinx dy dx _dx| %3D V1- y? 2 (x-…

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