Use logarithmic differentiation to find the first derivative. Enter your answer without fractional or negative exponents. y = #* xe* ニ dy

Q: Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x =…

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Q: 3. x2 + 2ху + 3y?

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Q: Find all points (x,y) on the graph of y = x-4 with tangent lines perpendicular to the line y = 4x +…

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Q: 4. y²tan y

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Q: A doll-manufacturing company wishes to create a display box with a square base and open front side.…

A: Let's find.

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. lim…

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Q: Question 4 When x°cos (x²)dx is evaluated using IBP, the value of J v du is? A B -cos (x2) cos (x2)…

A: We need to choose correct option.

Q: 9- x2 dx using Trigonometric Substitution what is dx ? x2 Consider 3 sec e de 3 sec? e de 3 cos e de…

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Q: 3x + cos r 2. Use Squeeze Theorem to evaluate lim I -00 VI+ a? – 5x

A: Solved below

Q: How many times will integration by parts be used in evaluating In'x dx? once twice thrice no need to…

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Q: d d Calculate ri(t) · r2(t)] and rı(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 2x4 + 3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? C(2x- 4) +D E(2x…

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Q: dx 4 sin e+C express the answer in terms of x. 3 Using Trigonometric Substitution (x² + x + 1) 2 4/3…

A: Given problem:-

Q: g(t) = 2t3 + 3t² – 12t %3D Find the intervals where g(t) is increasing and the intervals where g(t)…

A: Given: gt=2t3+3t2-12t   (a). To calculate the interval for increasing function, g't>0

Q: Using Integration By Parts, 2x² e3" dx = u v - |2x2 e3" dx = u v-, -Svau Find u v- Sv du · x3 e 3 dx…

A: Integral

Q: -4 Vx²+4x-5 Consider 1 dx, using trigonometric substitution find x. x+2

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Q: Find exactly T(t) and N(t) for x = e*cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: За — 1 (x – 2)(x + 5)

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Q: Find the sequence of partial sums S,, S2, S3, S4. and S5. 7 7 + 4 7 7 Σ = 7+ - 1 16 64 256 n = 1 S1…

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Q: Describe the graph of the equation. r = 7 cos ti – 18 sin t j+ k O An ellipse in the planex = 1,…

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Q: Vx2 + 4x - 5 dx = Using Trigonometric Substitution f(e)dA find the new limits of integration. 1. x+2…

A: Let's find.

Q: Evaluate the iterated integral. 6xy2 dx dy

A: We have to evaluate the iterated integral

Q: Consider (2x2- x² + x +2 x4 + x3 C D B + dx = dx find A+B+C+D- + x+1 O 3 O 2 O 4 O 5

A: Topic:- partial fraction

Q: Evaluate the integral 20 2) dr by making the substitution u 2. NOTE: Your answer should be in terms…

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Q: Write a in the form a = a- T+ anN at the given value of t without finding T and N. r(t) = (t + 5)i +…

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Q: x = 1– t- t - te [-2,2] y =t – t3

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Q: Sketch and determine the opening, vertex and focus of the parabola with an equation of y - 8x + 16 =…

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Q: A. Arcsec x - 25- xdx xdx B. 글x Arcsec x-를- В. C. * Arcsec x + 25- Vx -1 xdx xdx D. 글x + 글- Arcsec x

A: Given

Q: Evaluate the definite integral. V4x + 3dx 0.

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Q: Find the area bounded by y = x+ 4 and y = x2 - 2. Answer:

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Q: dt (t +7)

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Q: 2x3 – x² + x + 2 -dx = A + dx find A+B+ C+D- X+1 Consider x4 + x3 2 O 5 O 4 3

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Q: The loop of the following limacon is produced for which interval of the angle theta?

A: Given:       r=2+4sinθ The first step is to find the angular displacement of the inner loop. To do…

Q: f(x) – f(7) g lim x-7 x - 7 se symbolic notation and fractions where neede

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Q: dx The result of is F(b) – F(a), where F(a) and F(b) are both real numbers. What is the value of F…

A: integration

Q: Using Integration By Parts, x Arcsec 3x dx=uv- -Svdu 了 Find uv- x² Arcsec 3x – 2 dx 2 x²-1 3 x…

A: The given integral is: ∫x sec-1(3x) dx

Q: dy dx? Find in terms of x and y. x°-y° = -3

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Q: Integration by Parts Example 4. Evaluate In x dv,

A: The given integral is: I=∫lnxdx   As we know that; ddxlnx=1x

Q: Select all that apply: □ (5. 똥) □ (5. 플) O (5. -*) (-5, ) □ (-5. 똥) O (-5, -)

A: Polar

Q: /x²+4x – 5 dx Using trigonometric substitution, ƒ (8) dô. x+2 Find the new limits of integration.…

A: Given:        ∫14x2+4x-5x+2dx=∫abfθ dθ         =∫14x+22-9x+2 dx      Apply u-substitution.…

Q: 2 - V2r + 10 a. lim 1-3 r2 + x – 6

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

Q: (2x + 4) + 1 dx- x² + 4x + 5 x² + 2x– 10 2 (2x + 4) + 1 2 Consider dx = x2 (x² + 4x + 5) dx.…

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Q: Suppose that f(x) is a differentiable function satisfying the table below. 0 2 f(x) | 1| 2 | 12 | 7…

A: The objective of the question is showing that there exist at least one x=c for which f'(c)=5.

Q: Evaluate the indefinite integral. 15 +°dx

A: Given query is to eveluate the integral.

Q: Find the first partial derivatives of the function. x5 - y5 x° + y f(x, у)

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Q: If you are going to evaluate the integral S V1 - 7w-dw using trigonometric substitution, the answer…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 4x3 + 4x? – 2x + 4 dx - (x² + 1)?

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Q: 5. Use differentials to approximate the value of V(3.01)² + 2(0.99) – 3 in four decimal places.

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Q: dx Using Trigonometric Substitution J- 4 sin 8+C express the answer in terms of x. (x²+ x + 1) ² 4x…

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Q: s2+3 1. (s-3)(s+5)(s-1)² s2-s+3 s3(s+5)(s-2) s-8 (s-3)(s²+2s+17) (s+1)²(s²–4s+85) s² +5s-2…

A: let's solve option (2) L-1 s2-s+3s3s+5s-2 By partial fraction, s2-s+3s3s+5s-2=As+Bs2+Cs3+Ds-2+Es+5…