d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

Q: lim (4x - V16х? + 3х — 5 -Зх — 5 x00

A: Given :

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A: Given query is to find the limit of the expression.

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A: Here, the given vector equation is: F(x,y)=2x+xy-y2sin x+4

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Q: 20 For the sequence an n+1' its first term is 10 20 its second term is 3 its third term is 5 its…

A: Given :an=20n+1

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A: Solving

Q: dy 3x2 + 2 and dt dx Find 3 if y = – 2. at x - dt dx dt

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Q: Compute the derivative of the function y = 5 sin-'(x) at the point x (Use symbolic notation and…

A: We know, ddxsin-1(x)=11-x2

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Q: Nse Ithe me tsodl undetermined Cofficients to solve Ithe diffevential equation dy +ay = cos bx ¥a…

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Q: 12. Show that a rectangle with given perimeter has maximum area when it is a square.

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Q: Calculate r:(t) • r2(e})] and n(t) × ra(t)] first by differentiating the product directly and then…

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Q: x² – 1 Evaluate lim X +1 x2+3x-4

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Q: 3. Find the derivative of each of the following functions. Justify your answer. I sin z (a) f(x) =…

A: As we know that; The Product rule: f·g'=f'·g+f·g' The Chain rule: fgx'=f'gx·g'x   And…

Q: Q "- The value of e-(in+1)n is а) (-1)" e-я-1 b) (-1)"e" c) (-1)" e-*+1 d) (-1)" e- Q2 The period of…

A: e-ix = cosx -i sin x If y=A sinBx then period -2πB.

Q: Find solutions of the following equations by the method of separation of variables: 4. 2+= 0 at xe,…

A: 5.

Q: B2. dx Let g(?) = " 4t

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Q: Verify if the following vector fields are conservative: 2y 21 a) A1 = (1+æ²+y² > I+x²+y² b) Ã, =…

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Q: onsider the functionfx) 5x" + 8x 1. f(x) has a critical point at x ind the value of A: A, does f(x)…

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Q: Q 25-The Laplace transform of function f(t) = e¯'sinh4t is a) 2/(s²+2s) b) 2/(s²+2s+15) Q?-The…

A: To Find : laplace transform of f(t)=e-tsinh(4t)

Q: 1. limx→−1−  F(x)= 2.lim x--->-1+  F(x)= 3. limx-->-1  F(x)= 4.F(-1)=

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Q: 7. Let f(x,y) = x²y+ry. Find an equation of the tangent plane to the graph of f at the point…

A: The detailed solution is given below Thank you

Q: Ssinx j 4. sin x cos x dx 3.

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A: Solution: Given

Q: c. 2x³ + 7x² + 9x- 18; x+3 d. 6x3 + 11x2- 11х-16;B 3х?-х-3 1. Use long division to find each…

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Q: Find the first 4 terms, a10, and a,5 of the sequeñce with the following nth term. a = |(Simplify…

A: The sequence                        an=nn-3, n≥4 then we have to find the first 4 terms and a10 and…

Q: Question 8 Evaluate the integral below by interpreting it in terms of areas. In other words, draw a…

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Q: Consider h(x, y, z) = cos (xy) + eyz + ln (xz). Determine the directional derivative of h at the…

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Q: Describe the graph of the equation. r= 18 cos ti - 9 sin tj - O tis an ellipse in thez = 1 plane,…

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Q: The solutions of the equation (x + 5) (2æ – 1) (x – 3) = 0 are

A: This question is based on equating factors to zero.

Q: Determine whether n+1 converges or diverges. Give reasons for your answer.

A: Given: Here, an=n+1n2n. Notice that an=n+1n2n≈1n32. Now,                  limn→∞n+1n2n1n32=limn→∞…

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A: Solution is done in step 2

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A: Follow the procedure given below.

Q: 8. h(x) = (sin x )V tan²x + 1 %3D

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Q: 33 3.

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Q: True or False? Please explain your answer. S Edr = In z+c. a) b) c) f(z dr

A: As per guidelines we have to solve 3 subparts Please repost other questions again

Q: Use the Fundamental Theorem of Calculus to cvaluate (1 - da

A: Integrate using fundamental theorem of calculus.

Q: (6) In the interval 0 <x< 2n, the solutions of the equation tan? (x) = tan(x) are? (A) "/4 (B) "/4,…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Follow the procedure given below.

Q: 6) A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

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