11:32 E O1 令1 Using the substitution u = cos x, sin x cos3 x dx = .cos* x cos° x cos. * ) +C 4. 8. the above 6(2x) cos° (2x +C the above + cos"(2=1 +C .cos+(2x) cos (2x)

Q: -)Find the valne of cos 15°. Further s ho w thet Cos 15 <0. Conc lude thut Cos 15° 7 cos 15. (Note…

A:

Q: 4. 1+(sin (20))2 6 cos (20)d0 4. 1+ (sin (20))2 6 cos (20)d0 a f(u) du where g(x) =u, to evaluate…

A:

Q: Use a CAS to plot the implicitly defined level surfaces in Exercises 73–76.

A:

Q: Given the ODE (cscy)dx + (cos²x)dy = 0. A one-parameter solution of it is: O cosy + tanx = c siny =…

A:

Q: 3 Find the exact values of s in the interval [0,2x) that satisfy the given condition cos 2s = л 11т…

A: Topic : trigonometry

Q: 7) y=Flx)=cos" (x) A.) xCcoskl) =4 Cos? (x) %ax (coscx) =4 cas? (x) (-sin(x). 4 Cos (x)Sin(x) %3D…

A: Explanation of the answer is as follows

Q: 5. What is the exact value of cos(™)? y (0, 1) (二) (-1,0) 号 O 0号 01 19 () (-²,-²) )。 at trafte 135°…

A:

Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

A: Solution:

Q: in Let z = 0.5 +",., Find e 6z 3 C) e3 F) e-0.5 (cos 2 + isin2) A) -e 20 B) e-5* (cos 20 + isin20)…

A:

Q: To show that rπ/2 sin" x cos" x dx: (m - 1) (m- 3) ... × (n – 1) (n - 3)... (m + n) (m + n - 2) (m +…

A:

Q: 20. Which of the following is not an antiderivative of the function f(0) = sine cose? 1 A. B. 2 sin…

A:

Q: 1. Eliminate the Arbitrary Constant(s) of the following: 1. by xy'-1; b is constant, 2 y=+de; e and…

A: We have to eliminate the constant in the given equation. Here I am solving first two parts…

Q: Which of the following is a possible solution to y" + 16y = 0 O y = tan(4x) y = cos(2æ) O y = sin x+…

A: SOLUTION IS GIVEN BELOW

Q: 1. (a) Use integration by parts to verify the reduction formula cos" x sin x n Scos" xdr = -1 [cos"…

A:

Q: Use a linear approximation to estimate cos 29° Answer. The approximate value of cos 29° is O cos 29°…

A: Given, cos 29°

Q: S-) Find the general soluhon of sin'x y"-(25inx.cos x)y'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Please check step 2 for solution

Q: Which of the following is a possible solution to y" +ky =0 O y = ekz O y = cosk'a O y= k sinI O y =…

A: If roots of the auxiliary equation are imaginary i.e, α±iβ then complete solution is…

Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

A:

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0. {e' cos 2t, e' sin 2t}…

A:

Q: H.W: if w x2 + y2 + z2, x= e*Cos6, y-erSin0, z=e0 prove that aw/ar= er/w and aw/a0 = e20/w

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 3. Which of the following is the particular solution to the ODE. y" + 4y = cos(2x) 1 x sin(2x) 4 A.…

A:

Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

A:

Q: The value of the integral . rcos ydydr is cos 8 cos 4 b. - cos 8+ cos 4 2 1 c. cos 8 – cos 4 + Cos 8…

A: SOLUTION-

Q: 2n3+n² sin(n)+6 48. Calculate lim,,→0 312 cos(m10n 19: (Proof is not required)

A: Use the algebra of limits to find the limit of the given fraction, and use a concept that limit of…

Q: Find the exact values of sin and cos for sin e= on the interval 0° s es 90°. 2 sin 0.1691, cos…

A: We know that,  cosθ=1-sin2θ         cosθ&gt;0 in 0°≤θ≤90°        ⋯⋯1sinθ2=1-cosθ2…

Q: 13. Which of the following is the solution of [2x+ycos(xy) dx +xcos(xy)dy = 0 x² +cos(xy) = c b. x?…

A: By see this solution in below

Q: 21. a. e x = sec sin z sin z) (e sin b. Ve Cos 2sinz 1 U e sin z COS d. cos x √1-e2sinz

A:

Q: Consider (e cos 4 + ie sin 4) (11+12:) cos 4+ ie sin 4) (11+12i) 3DZ What is the general value of z?…

A: Euler's formula is given as that e^(ix) = cos(x) + i sin(x).

Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

Q: Which of the following is true for the BVP y" + 16y = 0, y(0) = 1, y () - = 5 with Yg = c1 cos(4x) +…

A:

Q: .2 Q3 Suppose that w = Jx2 + y² + z² e" cos 0, y = e" sin0 , z = re® Find aw and ar aw дө

A:

Q: 14. Which of the following does not require the use of the chain rule to find y y = cos ¹(10x5 - x²)…

A: Given problem:- Which of the following does not require the use of chain rule to find dy/dx? (A)…

Q: 4X^) Prove the reduction formula feese de n-2 cW Use part (a) to evaleate (cos2x dx Use parts (a)…

A:

Q: Q2// I= f, (x² cosx) use Simpson's 1/3 rules, with n=4.

A: We have to find the integral using Simpson's 1/3rd rule. In first question there is not equal…

Q: 3x If f(x, y) = e° sin 9y, then fry is given by: O - 27 e3* cos 9y – 27 e3 sin 9Y O 27 eša cos 9y 3x…

A:

Q: Which of the following is equivalent to: (e-2'e-t cosh t dt 2 L [cos h t] L [e* cos ht] O A.) B.)…

A:

Q: Which of the following is a fundamental set of solution of y" – 2y + 5y = 0. {e' cos 2t, e' sin 2t}…

A: The second order linear homogeneous differential equation is given by,…

Q: 10. If h(x) = x²2cos 2x, then h'(1) = A. 4cos 2 B. 2· 2cos 2x (1 + In 2) C. 21+cos 2 D. 21+cos 2 (1…

A:

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…

A:

Q: For how many a E (0, 1) will sin(x) + a sec(x) = cos(x) + a csc(x) have at least two distinct…

A:

Q: St² sin(2t*)dt A 1 (sin(2t*) – 2t*cos (2t*)) + C (sin(2t*) – 2t*cos (2t*)) + C 14 B D (sin(2t*) –…

A:

Q: Given that 7(1 + h) – 7(1) = (h - 1 + cos(h), e" -e-", In(2h + 1)) for all h where -. a 7'(1 :…

A: We will use the definition of derivative to find r'(1) as shown below

Q: Which one of the following equals (x + y) dæ dy. T/4 OA p2(cos 0 + sin 0) dr dð Зя/4 - 7#/4 " […

A:

Q: +1+C ,c.÷+ Q1: Choose the correct answer of the following 1. [ sin x dx is a. cos x+ C, b. -cos x +…

A:

Q: e work of a particle moving counter-clockwise around the vertices (2,0), (-2,0) and -3) 3e* F…

A: Greens theorem is used

Q: -1 (x³+y³ ,3. then xdw dw +y dy If w = tan x-y sin(w) sin(2w) cos(2w) None of these

A: