If (ds)? = (dr)? +2 (de)2 + r2 sin? e (doe, find the values of 1 3 and 13 (a) [22, 1] and [13, 3] (b) | 22

Q: = ? |c0,1,1) What is the x' In(=) +sin xyz +e = 0 O a. 0 O b. -2/e O c. e/2 O d. O e. -1

A: We have to find the partial derivative at given point.

Q: If 17e" +8 sin(x) f(x) = (e'3 cos(x)) f'(0) then f(0)

A: In this first we find f'(x) by using derivatives formula I solved complete in 2nd step

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Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: 1. y = x' sin? (2x2) 2. y = In (sec? e) 3. У%3D 1 xe4x 16

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: sinx S- cos?x+ 6cosx+13 O In cosx+3-Vcos²x+6cosx+13|+C O In cosx+3+/cos²x+6cosx+ 13 O…

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Q: d" y If y= cos x, then d x5 (A) -sin x (B) sin x (C) -cos x (D) cos x

A: This is a problem related to differentiation of the function. Based on the general formula and…

Q: Suppose that S"(ax + b) cos x dx then the value of a equals

A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: dy If y = x³ cos π, what is ? O 3r² - sin 7 -3x² sin T O 3x² cos T COS O-³ sin + 3x² cсos π

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Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: (10) The result of (D-3D D, +2D;)sin(x-2y) is

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Q: 10. 3 J√cos z sin ³ zdz COS

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Q: (c) Show that e* sin(x²)dx < e – 1.

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Q: S*r(sin³x cos x + sin x cos x) dx -- 4 Ja sin 50 de

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Q: =? |c0,1,1) What is the x* In(=) +sin xyz +ev = 0 y O a. -2/e O b. 0 O c. -1 d. O e. e/2

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Q: %3D 24. The number of solutions to sin (2z) =-2 sin r, where 0° <r<360°, is O two O four three O one

A: Given equation  sin(2x)=-2sin(x)  we use double angle formula  sin(2x)=2sin(x)cos(x)

Q: If ¹f [ 2³ sin ædæ = −2³ cos x + 3x² sin æ+ 6x cos a - 6 [ f(x)dæ, then f(x) = a. x cos x b. sin x…

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

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Q: If ſ x sin x cos x dx = xsin²x + Ax + B sin 2x + C, what is the value of A + B?

A: The given integral is, ∫xsinxcosxdx=12∫x(2sinxcosx)dx=12∫xsin2xdx=12∫xsin2xdx=12I1

Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: eVE cos(ev#) sin(evt) VE CO dt

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Q: S cos(7x + 5) dx = (sin(7x+5))/7 + c* O False O true

A: We have to evaluate   ∫ cos(7x + 5) dx

Q: Show that 0 π/2 st sin? xdx TT/2 [ 0 cos? rdr 2

A: A detailed solution is given below.

Q: Show | S a² sin®(e*) dæ| < 16n*. 8 Show | S, x2 sin°(eª) dx| < 3

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Q: S(2) = vāsin(5z) sin z

A: Differentiate w. r.t to x

Q: e csc 20 In (ecos 2 ) Ince cos CoS 20 28) Sin2 20 OP

A: Given integral is ∫ecsc2θlnecos2θsin22θdθ since lnex=x, so lnecos2θ=cos2θ The integral becomes…

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Q: 22. If y = (1- sin?x)i then y" is b. 1 COS X 2° а. C. - cos x d. -sin x sin x HIN HIN

A: The second derivative of the given function is solved in detail below.

Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: se 16) F(s)=- s+4 cos(21) Ans. f(1)= elsewhere

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Q: sin dx 32 cosS 35 4 Ssin +2 +c cos () • 32 cos + C 32 -cos 32 cos + C 7 4 32 cos 35 즐)-Scos()+기+C

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Q: d?y Suppose that y = sin? t and x = cos t. Then dx2 x=3 1 2 -2

A: Given: y=sin2t, x=cost

Q: What are the values of and cz so that y(x) = cq sin(x) + c,cos(x) will satisfy the conditions y(0)…

A: Given y (x) = c1 cos(x) + c2 sin(x)and y(0) = 1,   y'(π) = 1

Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

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Q: If g (x) = sinx dx and =3, then g (0) is equal to A) 2 В -2 4 D

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Q: -31 cosh 2t 7. (a) 2e- sinh 3t (b)-

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Q: Find dr/dθ in sin (rθ) = 1/2

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Q: Find all solutions to the equation: [sin(x)+ 1]2cos(x)-3]=0. Зп + 2nk, x = + 2nk, x = 11m + 2nk,…

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Q: dy Find , if Y = (1+ cosx)sinx dæ cos3x + cos³x – sin²x O cosx + cosx – sin³x cos2x + cos²x – sin?x…

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Q: Q2:- Find fo, fe , fo if f(p, 0,¤) = p² cos ¢ sin 0. cos O sin 0

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Q: Q/ IF y = Sim ܠܐ 10²² (4) y = 3/² sin(x) cos(x) Prove that

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Q: e* cos e* dx J 4 + sin²e* A 1 tan-1 2 sin e* + C sin? e* + C 2 2 tan-1 B sin e* tan- 2 1 tan-1 2…

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Q: If f(x) = (e'7 cos(x))' 18e +12 sin(r) f'(0) then %3D f(0)

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Q: If f(x) = 12sin(green wave), then the red wave isi %3D 20 |-3T/2 -TT T/2 TT 3h/2 2n |-10 IF f(X)=12…

A: Red wave satisfies the point -π2,0,3π2,0  a) Given,   6sinx+π+6 Put x=-π2…

Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: Find W (ex, cos x COs x sin x). B.) -2 (e) sin x cos X

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Q: dy is If y = csc (x³) then d.x %3D -6x² cos² (æ³) A sin? (æ³) -6x2 cos (x) sin² (æ³) B -6x² cos²…

A: Given : function y = csc2(x3)   To find : Derivative of the given function dydx?

Q: If f(x)=e^2x cos(3x), then f’(0) = ?

A: Derivative Question

Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

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Q: then If z=e sin 0 = ? О а. 1 O a. 2 Ob. 1 2i +2 OC 2i d. Od. 1 2. +2

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