1. S cot 2v dv 2. S tan*- dr 2 3. S (tan tan 5w +cot cot 5w )² dw sec (Inln x* ) dx 4. S 5. S Csc4 dx x2 tanzvx sec* /x dx 6. S 7. S csc*n y dy cot²n y 8. S 1 cot3 csczżdx x2 tan5 e-Ysecsec e¯y -dy x3 x2 9. S ey

Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0 %3D

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Q: 2x + 1 -dx (Зх -1) (г2 + 2х + 2) Evaluate: F (x) = 2 In (|3.x – 1|) – In (æ² + 2x + 2) - 4 arctan (x…

A: A detailed solution is given below

Q: 1 et dx 1 (1 — е*)2

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Q: Find y' if 4 cos x cos y = 3y. %3D

A: To find the derivative.

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: 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: +1

A: I have stated the used formula in the solution

Q: A triangular trough 10m long, 4m across the top and 4m deep is being filled with water at a afficed…

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Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

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: 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: dy by implicit differentiation. dx Given In xy+x+y=2. Find

A: lnxy+x+y=2Differentiate w.r.t x1xyxy'+y+1+y'=0xy'xy+yxy+y'=-1y'y+1x+y'=-1

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: (4x* – r*y +y*)dx + x*dy = 0.

A: Let's find.

Q: sin x xý + 3y += x2

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

A: To integrate the given function.

Q: Is Rolle's theorem valid for the function f(x) = Vi-x on the segment [-1,1]? a. No since the…

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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: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2 y =

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Q: d) (i) Use the alternating series test to show that the series converges. k+1 k +3 Σ-) k(k+1) k=1

A: To show that the given series converges using alternating test.

Q: Find the value of dt Oa 40 Ob.53 Oc 23 Od.13

A: ∫0∞e-3tdt∫e-3tdtSubstitute u=-3t→dudt=-3→dt=-13du=-13∫euduWe know that ∫axdx=axln(a)=eu

Q: 3 3 25x ? 2 7x3 3 16х5 dx 5

A: use property of integral to solve this.

Q: k=1 2K (c) Use the ratio test for absolute convergence to determine whether the series converges or…

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Q: The volume enclosed by the cylinders z= 5-x,z= 4x and the planes y = 0, x+ y =1. Solution

A: First we will draw the region and find limits for x, y and z

Q: Q3 Find y ン ニ月(^)→ t(メッ) tanx 2 y-(1+x)

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Q: dy Find the general solution of 2x² = a? + y? dx %3D

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Q: Suppose A = (a, 0, 2) and B= (6, –2, b), for some a > 0 and b> 0. (a) If projĄB = 12 24 =,0,), find…

A: Suppose A=a, 0, 2 and B=6, -2, b, for some a>0 and b>0.If projAB=125, 0, 245, then to find the…

Q: Using trigonometric substitution, given (Vx+64 dx, the simplified form of the integral is: sec³ed®…

A: We have to check whether the given statement is true or false.

Q: Which of the following is the general solution of the differential equation y" - 36 y=0 ? O…

A: y''-36y=0auxillary equation is given bym2-36=0(m+6)(m-6)=0m=-6,6m1=6 , m2=-6

Q: y = Vx* X

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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: 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 (s 2'ds Oa 2 1) In2 Ob. 2 (sln2 - 1) (In2)2 O. 2(sin2 - 1) (In2)2 Od 2° +1) In2

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Q: Let a = 2i – 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8…

A: Here we have to find the dot product.

Q: Find the derivative of f(x) = -2x Or) - 6x2 Of (x) = -6 x2 Of (x) = -6 x3 %D Or-6x* f (x) = 6 x4 %3D

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Q: V9 – 4x2 -dx Evaluate: x2 6/ 4x2 + 2x sin A f (x) +C 4x² + 2 sin () + C -1 V9 f (x) = B 3 None of…

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Q: How/ Find the General solution for dhe following O e %3D

A: The given differential equation is;  e2x(dy+2ydx)-x2dx=0. Repost the next questions.

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

A: limit continuity differentiability at x=4

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

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Q: 5.Find all the first partial derivatives of each function f (x,y) =(2x– y)* а. 3/2 S(x, y)= (4x–…

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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: Give the VALUE only. No need to inclu unit. *

A: Given: s=24t+10t2

Q: Consider a function () whose dertvative ') continuous as shawn below Graph of f'(x), NOT f(x) 1 5 -1…

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Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) *+ 2y = 3 ,y (0) =…

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Q: a. f(x) = 4x + 11 find: f'(-2) b. f(x) = 2x2 5x 3 find: f'(2) |

A: We have to calculate value of derivatives function for the given x value.

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: Find the derivative of f(x)= (In x O a. 6x(In x) O b. 24(In xỷ c. 24 In x O d. 12(In x)

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Q: 4. Find the area of the region that lies under the graph of f over the given interval. a. f(x) = 2 -…

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