TVy+1-2 dy can be evaluated conveniently if we let x=VVy+1-2 and dy = 4x(x² +2)dx. T True F False

Q: Find the value of t for which 1 V3x+1 O none of the choices 6 O 3 O 5 O 4

A: Here, given that: ∫1t13x+1dx=43

Q: Question 8 x2 + 64 Using trigonometric substitution, given - dx, the simplified form of the integral…

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Q: sin x xý + 3y += x2

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Q: Q2) Solve the D.E dy - (2x/1-y2)dx 0 %3D

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Q: y" + 4y" + 4y' = 0. %3D

A: Follow the procedure given below.

Q: Write T if the statement is true, or F if it is false. W. 1. -dx x' +C 3 %3D 45x=-5x +C 9. 2. %3D 4…

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Q: I. Evaluate the triple integral zdV, where E is bounded by the cylinder y? + z? = 16 and the planes…

A: Let's find.

Q: Determine the slope of the tangent to the curve y – 3.xy +2x =4 at the point (3, 2).

A: curve :  y2-3xy+2x2=4differentiating w.r.t…

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: dy 1 y? +y 3

A: We have to integrate.

Q: Using implicit differentiation, find the slope of the tangent line at the point (9,16) on the curve…

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Q: cos 2x sin'x dx can be evaluated by factoring sin x as (sin?x) 2sinx and transform sin?x into 1-…

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Q: :(7e*) cos (4e") dx Evaluate: e cos --cos (3e*) – cos (1le*) + C 22 ® os (3e*) +cos (11e)+c COS 6.…

A: We have to find value of given indefinite integral

Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: 1. The graph of a function y = a/b(x-h)+k shown below. -1 -40 Algebralcally determine two different…

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

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Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: Find if yvx – 8 = xy + 2.

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Q: Eind the limits lim hth G h Sinshe-Go

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

Q: Consider the series 0 n=1 2+n3 For what values of p does it converge? I. p> 1/2 II. p< 2 O l only O…

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Q: Evaluate the following integral using three different orders of integration. SSL:(x: – y') dV, where…

A: Here we have to evaluate the given integral.

Q: -6x-'dx

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Q: (x²y + 2xy² – y³)dr – (2y³ – xy² + =*)dy = 0.

A: Solving

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: All continuous functions have antiderivatives. If f and g are continuous on a <x < b, then "Ư(x) +…

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Q: 10re", a 0 (a) Identify all critical numbers of f. (b) Determine the extreme values of f on [-2, 2].…

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Q: Q3) Evaluate triple integral y(x2-y?)dz dx dy.

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Q: Q3) Evaluate triple integral (x2 - y?)dz dx dy.

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Q: wo linearly independent solutions of the differential equation y"-4 y=0 are O y,=e** and y, = e 4x…

A: I am attaching image so that you understand each and every step.

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: Q3) Evaluate triple integral f, L(x - y?)dz dy dx.

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Q: *) dx Evaluate:

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Q: ) Evaluate f'(x)dx.

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Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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

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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: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

Q: irvature and the radius of curvature at the stated poi r(t) = 6 cos(t)i +6 sin(t)j+ 7tk; t= 2 r the…

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Q: Let a = (1,2,3),b = (4, –3, –1),c=(-5, –3,5) and d = (-2, 1,6).Find: %3D а. а+ 5b b. [7c| – |5d| c.…

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Q: Q3) Evaluate triple integral f x - y²)dz dy dx.

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Q: Is Rolle's theorem valid for the function f(x) = V1- a. Yes. It is valid in this range b. No. It is…

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Q: The global maximum of f(x) = x-4x over the interval -2sx<3 occurs at what value of x? O a. X = 3 O…

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Q: Find the derivative of the function f)= [sec() 6 sec-1 xVx2-9 1 sec x Vx2 -9 O 3 sec-G) 3. xVx2 -9 3…

A: In this question we have to find the derivative of the given function.

Q: Question 13 - [x²/25+ x²dx , we let x= 5sine. (T True F False

A: We have to find integration

Q: e-2 1 Evaluate: e-3 xInx Oc -In 6 O d. In 6 2/3

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Q: applying substitution méthöd: sqns -48

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Q: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: 12x 3 3 15 12 x4

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

A: The given curves are; y2=x &amp; x=2y-y2   Now find the point of intersection between the curve y2=x…