Question 1 9- 4.22 Evaluate: (A) 9 – 4a² + 2 sin-' () +C f (x) : B 9- 4x2 – 2x sin f (x) = V9 – 4.x2 + 2x sin (E) 2+¢ C f (2) : O f(x) 9- 4x2 – 2 sin (4) +C D f (x) = E None of the given choices

Q: 2.Find the indicated limit or state that is does not exist x* – y* C. lim (x,y)→(0,0) x² +y ху d.…

A: Solving

Q: Example -3 .2 Evaluate I (x+ 2y – z) dx dy dz I (x + 2y – z) dx dy dz - 2 SLE + 2xy – xz dy dz - 2…

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Q: Find the derivative of the function f(x) = csch () () -2 coth csch 2 2 -2x coth csch -x coth csch 2…

A: L

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

A: tripple integral  First we will integrate w.r.t z and then w.r.t. y and then w.r.t. x.

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

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

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: (3-y Q1) Evaluate the integral dx dy using polar coordinate

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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: 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: Hond / Find the solution for dhe fllowing = e @ siny d9 = osy(l-xGsy) (2) %3D Siny Cosy x = e de dy…

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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: dy Find if yJx-9 =Xyt2 %3D

A: we have to find dy/dx

Q: Evaluate (s 2 ds Oa.2 sln2-1) (In2)2

A: ∫ s· 2sds=2ssln2-∫2sln2ds=2ssln2-2sln22Add a constant to the solution=2ssln2-2sln22+C

Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: 2x 4. Given the function F (x)= 3 do the following: 4.x +1 a. Find F-1 (x). b. Find dom F and dom…

A: Given,            The function is Fx=2x-34x+1.

Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

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Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: Evaluate the definite integral. e12. i+ k 12 e12 i-elj+; k 12 e12 -1 12 e12. k 12

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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: 3rd derivative of y sin 3x

A: Here we have to find the 3rd derivative of           y = -1/sin(3x)

Q: 12x 3 3 15 12 x4

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Q: Example Evaluate +f -P) dpdgdr (p2 + q² – r²) dp dq dr + pq² – pr2 dq dr 3 1 + q? ² – r? } dqdr 3 -…

A: Let's find.

Q: In solving the antiderivative of f(x) = 2- 3sin(x) by miscellaneous substitution, the substitution…

A: The function f(x)=12-3sin(x)

Q: Find the general solution of the following differential equation: y" + 4y" + 4y = 0. %3D

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

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Q: If f(x) = 2x + Ax?+ + Bx – 5, find the value of A when f(2) = -3 and f(-2) = -37 -5 -3

A: A=-15/4

Q: Find the equation of the tangent line to the curve y =4x-8 at the point (3.-2).

A: Topic = Derivative

Q: A solid right cylindrical cement block of volume 97 ft³ is to be made, and then painted except for…

A: Follow the procedure given below.

Q: Evaluate the triple integral. SSSE2.xy dV , where E lies under the plane : = 1+x + y and above the…

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Q: Evaluate f Vr+ V?dx Oa. 3 am +2) +C (V2) +C can) Ob. 2 am +2) +C 30 om +C (25) Oc 2 an +m) +C O d. 5

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 Ju. (v x w)| to determine…

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Q: *) dx Evaluate:

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Q: dx :Ja-4)(x-1) Evaluate: 1 A (x-1) + C X- 4 B None of the given choices x- 4 + C х-1, © 3ln

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Q: The integral 4 dy dx is equal to: Select one: 12 6. None of them

A: To determine the value of the integral ∫03∫014 dy dx.

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

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Q: b + c =? с — 2а 4a = 3b, 5b = 3c =

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Q: y = Vx* X

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Q: 2BVC = (12x - 24)° and mZEVD = (2x + 15. What is m2CVE ? THAM V. A D. Find the missing pieces.

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Q: %3D /Q5) Find volume of body bounded by z2 +y2 + x2 = 4.

A: To find the volume of the body bounded by z2+y2+x2=4.

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

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Q: 10x ME 10. 4+ 25x'

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Q: Question 8 In |x³Vx2 – 625 dx , if we let x = 25sece , then dx = 25secede. True F False

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Q: Which of the following is the Taylor series expansion of the function -x2 with center at 0. f (x)=e…

A: Given problem:-

Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: n(A U B) = 25, n(A N B) = 5, and n(A) = 20 Find the value of y. A В 5 y Your answer

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Q: !. Find the numbers, if any, where the function f(x) is discontinuous. Explain your answer. x + 1…

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Q: Evaluate +V7dx 3 Oa.5 +C 2 5 3. Ob.2 3 2 Oc 2 sm +- Ot ast Od +C 3 2 52~

A: Evaluate integral

Q: Describe the largest set S on which it is correct to say that f is continuous хx* + ху — 5 а. f(х,…

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Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

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Q: Question 6 Evaluate: VA 4 – a² A None of the above 2 sin () – av4 – a² + C f (x) 4 sin- (E) - æv4 –…

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