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Q: 1.f In(x² +a°) dx Ans. x In(x' +a')- 2x + 2a tan " +C a

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Q: 2 X+ 9x + 2 x3 +2x? -x - 2 dx

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Q: 9. A triangle has two sides represented by vectors OA = (2,-3) and OB = (3,1). Determine the…

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Q: -2+0.5-0.125+...= (Write your final answer in fraction form, when applicable)

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x3 +x)dx

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Q: a) fx² sec2

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) sin(9t), lim t-0 e5i +…

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Q: (a) Use Green's Theorem to find the line integral over the simple, closed curve C : r(t) = (cos t,…

A: To use green's theorem to find the given line integral over the curve C

Q: x² + 4x + 1 dx (x – 1)(x + 1)(x + 3) d* - Inlx- 1+Inlx+11- n|r+ 3| +C Inlx- 11+Inlx+1| +Inx + 31 +C…

A: Let's find.

Q: 2. True or False? a) -2(3BA)and 6AB'are equal vectors. Justify your answer. b) If |AB| = |AC|, then…

A: This question can be solved using the concept of equal vectors.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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

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Q: Find the exact value of: 1 + cot (Write your answer in the simplest form, use fractions whenever…

A: Trigonometric values cot2π6=32=3 sec2π4=22=2

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e2x –…

A: Solve the exponential equation algebraically.

Q: Write down the first four terms of the sequence given by x, = 3" + 2", starting from n= 0. X1 = X2 =…

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Q: Find the volume of the solid bounded by the cylinder x2 + y2 =16 and the planes y=z, x=0, z=0 in the…

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Q: (c) f(x) = sin? x [Hint: sin? r = l-cos 21] (a) f(r) = r arctan r b) f(x)=x²e- %3D

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Q: is an angle in standard position, tan(e) 0, then the terminal side of lies in which quadrant? A IV…

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Q: Use continuity to evaluate the limit. 16 + Vx lim 16 + x

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Q: C. y = cosh¯'(x² + 1) + tanh-1(sinx) + sinh-'(cothx²)

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: y = In (csc 2)

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Q: Evaluate the function at the given value of x. Round your result to three decimal places. Function…

A: Solve the given

Q: testconuer gnce and diverg ence 2+5 3"

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Q: nvestigate the convergence of the following series. H.V 2n+5n 2) Σ-1 3n %3D1 1LJ!

A: We have to find out convergence

Q: Use the properties of the derivative and the given vectors to find the following. = ti+ 8 sin(t)j +…

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Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: 11 ti + dt

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Q: 13. Compute the Laplace Transform of f(t) = t°e" +e* sin3t. 4 1 A) (s+ 2)'s² +4s + 13 2 B) (s –…

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Q: :. Let x(t) = 2 sinh t , y(t) = cosh(t²) be a curve in the Oxy-plane, given in parametric form. (a)…

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Q: For the cruciform in the figure below, the equation is x²y2 - 9x2 – 4y2 = 0, find the equation of…

A: To find the equation of the tangent line for the given curve.

Q: o<×くT ② Foのコ 2 [:

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Q: Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its…

A: We have to find out

Q: Determine the amplitude, period, midline, and phase shifts of the function. Then write the equation…

A: Given problem:- Determine the amplitude, period, midline, and phase shifts of the function. Then…

Q: Use the divergence theorem to find the outward flux of the vector field F(x,y,z)=3x2i+1y2j+2z2k…

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Q: For the function f(x) = - 2x-3, do the following. (A) Find the average value of f(x) on the interval…

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x)

A: Given Data: f(x)=5x+112022 Formula used: dax+bndx=nax+bn-1dax+bdx dxndx=nxn-1

Q: A small resort is situated on an island that lies exactly 4 miles from PP, the nearest point to the…

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Q: 4х Consider the function A(x)=2x+ for x > 3 Зx-1 (a) This function has one critical value larger…

A: We will start from critical points and follow upto inflection point

Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: 7. 1 (x dy – y dx) = 0 %3D x² + y²

A: Here, the given DE is: 1x2+y2(x dy -y dx)=0...(1)

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

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Q: i 15Y4 + 32X+ 23x?+ 25X-3

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Q: v (km/hr) t (hours) -b The figure above gives your velocity during a trip starting from home.…

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Q: 1 :? 5+ x² Which of the following is an antiderivative of the function f(x) : %3D (a) 2x In(5 + x²)…

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Q: . Find all relat/ve extremo and saddle points of the runcton. Use econd Partials Test where appliı…

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