If x = 3 sin t and y =2 cos* t , then find dy at t = dx 4 O a. -0.67 O b. 0.76 O C. 0.56 O d. -0.86

Q: Given: [ Scos(cos2x) sin2x dx Find: du O 2cos2x dx O -2sin2x dx -2cos2x dx O 2sin2x dx O O

A: ∫coscos2xsin2xdxLet u=cos2x.So,     du=-2 sin(2x) dx

Q: 1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

A: To evaluate the given definite integrals.

Q: If z = x?y + 3xy, where x = sin 2t and y = cos t, find dzidt when t = 0.

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Q: Lind dy/dx Sin x 1- CosA 2. Sin n4 fos H Cos n

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Q: [et Suppose A(t) =0 0. cos t sin t, show that A(t)-1 exists and then find it. - sin t Co t. -

A: Given- At = et000cos tsin t0-sin tcos t To Show- Show that At-1 exists and then find it.

Q: Given: x = 0 – sin 0; y = 1– cos 0 d'y Find: dx?

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Q: Given dy find 36 Cos 6x y' dx sin 6x + c 6 sin 6x + c O-6 sin 6x O-36 sin 6x

A: here option a is true.

Q: e n'rdr 17 cos'x Sin 2. 4

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Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: (b) S¤(tan? #)dx (c) S cos(2t)e'dt (d*) S(arccos x)²dx (e*) S (1+ 3x)2 dx Hint: Check for a similar…

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Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: (a) e3 sin 2x da sin 2r (b) x* In x d.r (c) sin r cos rdr 3. (6)

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: dx = 1– cos(bx) Select one: a. br – In sec(bx) + tan(bx)| + C b. – csc(bæ) – cot(bæ) + C - - In |1 –…

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Q: dy If x = a (0 – sin 0), y= a (1– cos 0), then find dx |

A: Introduction :

Q: The result of dy/dx for the following function is COS X y = 1+sin x

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Q: Given æ = 2 cos t + 12 and y = 6 sin? t dx (i) dt dy (ii) dt dy (iii) dx || ||

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Q: . Find L(t cos at } .

A: We will be using the known formulas to arrive at the final answer.

Q: 9. dt + 을 = COS t + Answer: s = sin t + 을..

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

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Q: dy and y= cos't then dx If x= sin?t O -1 O 2 O None of these O -2 1

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Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: 20. sin nx dx + f * +[ cos? nx dx , where n is any real number. A. 0 В. 1 С. т D. 2 T

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Q: If x = t +cos t, y= sin t, find d^2/dx^2

A: Given that      x=t+cost , y=sint  Here we have to find d2y/dx2 .

Q: If x=3 sin e, y=9 cos e, then at e =0 is dx O a. 0 O b. 3 O C. -3 O d. 6

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Q: O Find the inde frinite in tgal 曲 A cos (2¢) df

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Q: Given 5y + cos(3y) = x³ Implicitly find dx Select one: 3x Sy²+sin 3y a. 3x O b. 5y²-sin 3y C.…

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Q: Find g(e) so that when u = g(x) the integral S: 1+lnx sec(g(x)) dx can be rewritten as ſ cos u du .…

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Q: d (c) (cos(2²) + In(3 – 2æ)) dx

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Q: de 6) S 7) S(1 – sin? 3t) cos 3t dt 8) ſ tan (5x) sec?(5x) dx cos? e

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Q: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

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Q: sin 2ax Given ſ cos? (ax)dx : Calculate the following definite integral f cos2 (0.5x)dx. 2 4а

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Q: Find dy/dx in the following: -1 2. Y= cos cot x

A: The given function is: y=cos-1cotx           From the property of inverse trigonometric function, we…

Q: 4. J e3x cot e3x dx. 5. J dx/cos?x. dx 6. S sin? * 2

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Q: 6. S sin*(e³*) cos(e³*) e³× dx

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Q: The general solution of the DE dx = cos?y is A y= sec?x В y=tanx + C y=tan-1(x) + c y= cos os-(x) +…

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Q: Find dx implicitly, if e*(e♥ – 1) + sin(2x+ 5y) = In(v7) – dy 5 ·cot(2x - y+2

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Q: given dy=x+coS X find yuhere y( -1.

A: Using variable separable.

Q: Find the given 5x? cos 2x dx. Using this: "uv – f v du"

A: NOTE: Refresh your page if you can't see any equations. . use integration by parts take

Q: Find the first two positive solutions to 2 cos(t) t =

A: Trigonometric equation: - Trigonometric functions are used as variables in trigonometric equations.…

Q: Solve the following Bernoulli's equation by using an appropriate substitution. sin y (x + sin y)dx +…

A: We have to solve the give Bernoulli's equation by substitution.

Q: Find dy/dx for the following 1) y = x3 + sin x? + sin-1 5x

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: dy If x = 3 sin t and y = 2 cos"t, then find at /= dx Oa0.76 Ob.0.86 OC 0.67 Od.0.56

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Q: 3. Evaluate L{4e¬2tt3 +t sin t cos t}

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Q: Find dy/dx of the following: a. y=sinh-5x b. y=sinh-e* c. y = cosh¹ √√x

A: To find dydx for the given y.

Q: If V) AT sin (2 Tf t)/(2 TfT), find the energy contained in v (t).

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Q: 7π| A d) S_T/A (sin x + cos x) dx

A: We will evaluate the given integral in the following step.

Q: D. ( [ 3° cos"(5t) dt sin(z)

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