r(t) = (4 sint- 4t cos t,4 cos t+ 4t sin t), for 0sts, 2

Q: Approximate (a) cos 0.8 and (b) cos 1/2 using the linear approximation technique

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Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: 2cos'z = COS T Select all correct solutions.

A: Follow the procedure given below.

Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

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Q: Find d(tan x)>dx.

A: dtanxdx

Q: f (t) = 4 cos(4t) – 9 sin(4t) + 2 cos(10t) (As* + Bs3 + Cs² + Ds + E) Fs) Fs4 + Gs3 + Hs² + Is + J

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Q: dw Use the Chain Rule to find where w = cos 12x sin 4y, x = - dt and y = t". 4 dw

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Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

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Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

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Q: b) Solve to find if y = Tant VE and t = 4x-2 – secx dz b) if z = sin20, and 0 = [cos(w) + 1]² + cos…

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Q: 4x3 — 2х2 — х+5dx А. -2 TT 3 sin t 4 dt cos²t В.

A: Evaluate the integral using the second Fundamental theorem of calculus.…

Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: y" + 4y = 4 sin(2x)+ 8 cos(2x), y(0) = 0, y' (0) = 1.

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Q: f(t) = t/ 4t2 + 1, sin(t) cos² (t), for t eR t2 +1

A: In this question, we find the equation of tangent line at t=0 for the given curve f(t) and in the…

Q: derive 8t sin t (d) s %3D cos t t5

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

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

Q: Differentiate y = sin (e) 3x O a. 3e3 cos e3 e3x O b. es cos e c. 3e2 cos e2a Od. O d. 3e" cos e

A: Recall:  Chain Rule of differentiation :        If f and g are both differentiable , then…

Q: S(1- cos )´sin ź dt, u = 1 – cos 4. U = V5x+8' dx ,u 5x + 8

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Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: L(cos at) = %3D s2 - a2 صواب İhi O

A: Given that  L(cosat)=s/(s^2-a^2) To find the condition is true or false

Q: cos e de =_ %3D • 2 • -T • 6

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

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Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: What is if z = x'y+ sin(xy²)?

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Q: f (t) = 4 cos(4t) – 9 sin(4t) +2 cos(10t) (As* + Bs3 + Cs² + Ds + E) Fs) Fs4 + Gs3 + Hs² + Is + J

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Q: 3. Given that z = e" cos (), u = 4e2" – sin 2y, v = e" + n tan r. COS - Use chain rule to find dz/ðx…

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Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: Utt || for 0 < x < T u(x, 0) = x? u:(x, 0) = }cos(8x) Uz(0, t) = u„(r, t) = 0

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Q: dy Given that y =÷-sin3x . Find de 2 18. 4 +3cos 3x A B 4 -3 cos 3x 4 3 cos 3x C +3 cos 3x O A Ов

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Q: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

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Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

A: solution

Q: Obtain the der a) cos(xy)=2y, find y'

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Q: Integrate f,-¿ S=; cos x²dx dy =1 (x= 1 y=0 Jx=y Select one: a. cos1 b. .5cos1 C. sin1 d. Non of…

A: We will find out the required value of given integral.

Q: (b) Determine J cos(x²) 2x dx by using substitution method.

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Q: Hf sin x = A + B cos 2x +C cos 4x, then A = %3D C =

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Q: -2x 2) (² f(x, y) = e¯ fxx + fyy = 0 Consider -2y cos 2y - e cos 2x. Verify that

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By…

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Q: I need help understanding this calculus question

A: To compute the value of the integral over the curve C.