Find the derivative of f(x) = In [sin(x) +x] Lsin(x)-x] %3D 2(sin x – x cos x) x2 - sin? x )2(x cosx - sin x) x2 – sin2 x O 2(x sinx- cos x) x2 - sin2 x 2(cos x- x sin x) x2 - sin2 x

Q: inside polar functionr = 2 and outside p in third auartor

A: We have to find the area according to the given information

Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

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Q: 12t – cos 31) dt sin7t sin4t dt = A True B False

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Q: dy Given 4x -9y =1. Find by implicit differentiation. dx

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Q: A line is drawn through the point (6,4,2) perpendicular to the yz- plane. Find the coordinates of…

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Q: A. Evaluate the limit of a function using the concept of Special Limits. 1. lim t→0 t t2-3t+5 + t2-1…

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Q: Q2) Convert the polar function r = tan20 to cartesian. %3D

A: Let's find.

Q: x² + 2y? + 3z² 18. lim (x, y, 2) →(0, 0, 0) x² + y² + z?

A: We have to find the limit by two ways method

Q: Q2) Convert the polar function r = tan20 to cartesian

A: We know that x = rcosθ, y=rsinθ Given: r=tan2θ

Q: Find the Area bounded by the curves y = x and x = 2y – y?.

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Q: x² – 25 S The antiderivative of dx is V x2 – 25 – sec-lx+ C. A True В False

A: follow next step

Q: Q4) Find plane area inside the polar function r = 2sin E- 0) and outside r= sin -0) in first…

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Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: g"(x) sin(x- 1) x-1 -4 13 A(x) = kr -8x + 6, -1 10 x>3 8 3 -1 (E) Find all x value(s) on the open…

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Q: Find the maximum point for the function f(x) = 1 + 12x – 4x O (-1, -7) O (2, -7) O (0, 1) (1, 9)

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Q: 24. dx AX

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: *) dx Evaluate:

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Q: The triangle ABC is defined by the vertices A(1, -2, 2), B(1, 4, 0) and C(-4, 1, 1). Let M be the…

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Q: Evaluate fs 2°ds O a. 2*(sln2 - 1) (In2)2 O b. 2(słn2 - 1) (In2)2 O C. 25 - 1) In2 O d. 2° (+ 1) +1)…

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Q: 5 – 2x dx V5 + 4x – x² Hint: 1+4 = 5

A: To integrate the given function.

Q: 4. Find the Laurent series of the following function : f (z) = (z + 1)(z + 3) 1 region 2 < |z – 1| <…

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Q: Q3) Find the Area bounded by the curves y? = and x = 2y – y².

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Q: a. Draw the fuunclion y=1x1/

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Q: The graph of a function f is shown below. YA f a Graph b 1. Which grap is an antiderivative of f?

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Q: Let y=f(x).Which of the following correctly defines dx [fk+Ax)-fw] a. lim Ax+xL Ax Ob. lim Ax+x…

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Q: (1 f(x) ={ 5 if x = 4 at x = 4 if x + 4 x - 4

A: limit continuity differentiability at x=4

Q: Evaluate: | (cosh²2r+ sinh²2r) dr (A 2r +C 1 -sinh 2r +C 2 B -sinh 4r +C 4 D r +C E None

A: cosh²(2r)+sinh²(2r)= cosh(4r) ∫cosh(x)dx= sinh(x)+C, C is a constant.

Q: Water is pouring into a swimming pool. After t hours, there are t + sqrt(t) gallons in the pool. At…

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Q: What is the derivative of f(x) = tan-(x)? %3D

A: We can solve this as follows:

Q: d d. Calculate ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt dt the product…

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Q: 3 3. Given the graph of the function ƒ(x)= (x+2) a. Give a step-by-step explanation of how to graph…

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Q: [3-x 2 2 2 4 - x -2 -4 -1 - x. 0,2 O 0,3 O 2,4 O 1,3 1,2 O

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Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: Question 3 2 dr sech 2r = A True B) False

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Q: Differentiate the following functions. Show your complete solutions and emphasize your final answer.…

A: 1) f(x)=25x    Differentiate with respect to x   f'(x)=252) f(x)=-4x5+2    Differentiate with…

Q: Find the average value of the function f(x)=e" on the interval (0,4) Da 3725 Ob 490 OC 745 Od 186 25

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Q: Q1) Evaluate the following integral using Partial Fractions Method: y = : x³ +x? dx х2 +x — 2

A: Given: y=∫x3+x2x2+x-2dx   We know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: Differentiate Derivative of outer function  Derivative of inner function Differentiation  1. y = sin…

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Q: Question 2 Evaluate: J y* sech (e m)tanh (e ) dy A sech (y7) + C B) None © -eh*(,) + C E

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Q: 8. (a) Use the limit comparison test to determine whether the series converges. k=1 (b) Use the…

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Q: Q5) Find volume of body bounded by z2 + y2 + x2 = 4.

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Q: Q5/ Use Linear Regression to fit the following data: 1 3 4 Y 4 9 10 10 8. 00

A: Follow the procedure given below.

Q: 1-y -x. dy at the point (0,1) given the curve dx Find the value of 1+y

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Q: Which series converge in the interval described by x|<1? I. 1+x+x²+ ... I. x+x³+x5+ ... O I and II O…

A: See the answer below

Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 + x – 2

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

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Q: "u,V.w are three vectors such that each is incined at an angle of 4 with the other two, and that lul…

A: To find the scalar product of two vectors with the given conditions.

Q: If f(x) = (2x) , find the derivative of the function Or) = f'(x) = 3(x)0.5 f'(x) = -(x)0.5 f'(x) =…

A: 1)f(x)=(2x) -0.5 2)f(x)=(1+sinx)/(x+cosx).

Q: Describe the graph of the equation. r = 18 cos ti + 4 sin tj -k O Itis an ellipse in the x = -1…

A: Let's find.