2 Without using technology, sketch the graphs of the following for 0°

Q: Find the quadrant in which the terminal point detemined by t lies. sin(t)<0 and cos(t)<0…

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Q: ds 53. dt = 8 sin" (+ + 12). s (0) = 8

A: Given : dsdt=8sin2(t+π12)s(0)=8 Solve the initial value problem multiply both sides by dt then…

Q: Find the lengths of the curves x = 8 cos t + 8t sin ty = 8 sin t - 8t cos t,0 ≤ t ≤π/2

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Q: 2 X(+) = SIN'セ y (t) = Cos?t 9) IF dy FIND %3D

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Q: Solve the following equation using the Galerkin's method (at lease 2 parameter solution). Please…

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Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

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Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: -똥, V5 with s in quadrant Il and let sin(t) 4 8) Let cos(s) = -, with t in quadrant III. Determine…

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Q: Given that Sinh Ys 2. fnd sech x, eanh y with draw atiangle

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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: Find a particular solution to y" + 36y = 24 sin(6t). %3D

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Q: (e² sin*(2r)' 21² +1 , y = In

A: Use the lograthim rule of derivative and than with the help of chain rule calculate the derivative…

Q: The length of the curve y= In(cosx) between X=0 and X = TT/3 is given by: a. None of the other…

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Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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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: Using Simpson's rule, the approximation value for the o sin(x)dæ is : Select one: a. 1.024 b. 0.425…

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Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: TT/2 S,"/e cos?x.sint x dx in tegralinin bulunvz sonucunu

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Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

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Q: Find the length of the curve 7 (t) = (3 cos(4t), 3 sin(4t), 4t) for –5 <t< 8 Give your answer to two…

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Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: solve for y in terms of t or x, as appropriate.

A: Solve for y in terms of x :     lny2-1-lny+1=lnsinx

Q: c fx) = at (4, 2) 3x – 4 d y=x In x at (0, 1) sin3x at y =- x? 4 e T 2

A: Part(c): Given function is, fx=x33x-4 at 4,2 To find the gradient of a function (which is a vector),…

Q: s(t) = 40 sin 2t at t = 0 %3D

A: Given position function

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

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Q: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

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Q: dy - y = x? sin(x) dx

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Q: /4 sec? Vwdw a) b) sin 2.xcos xdx c) f tanh xdx

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Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: None of the choices…

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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: On what interval is the solution of the IVP cos e (1+ sin 0) y (0) = 2 - 47 valid?

A: Given IVP is dydθ=1cosθ1+sinθ y0=-12 Now,  dydθ=1cosθ1+sinθ dy=1cosθ1+sinθdθ∫dy=∫1cosθ1+sinθdθ

Q: What is the general solution of sin z sin ydx + cos rcosydy 0? %3D

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Q: - ual2) V17 – cos(27at) (2 – 4t) sin(#) Given f(r) = edt, find the equation of the line tangent to…

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Q: Find the value of dw/ds at s = 0 if w = sin (e^(sqrt(r))) and r= 3 sin (s + p/6).

A: Find dw/dr using chain rule.

Q: Find the length of the curve [x = eª cos(t) y = et sin(t) for 04 (Hint: You can simplify the…

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Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: 2. Find sin(72) -dz. where C: z(t) = 2 cost+i (2 sint). Os ts 2m.

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Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

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Q: Let y = cosh(ina²) then find y'. Oa. sinh (2a.tra) -1 Ob. O b. O c. - sính(Inz²). 2 O d. - sónh(2a.…

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Q: 2. Prove the following equation is exact and hence find its general solution. (y?sinx + xy?cosx)dx +…

A: Given: (y2sinx + xy2cosx)dx + (2xysinx)dy = 0 To prove that the above equation is exact. We also…

Q: Given the implicitly defined function 6. cos (2*y) – y* - cos(2r) – y? dy and dr dr find at the…

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Q: Find the value of dw / ds at s = 0 if w = sin (e√r) and r = 3sin (s + π/6).

A: w=siner,  r=3sins+π6 Differentiating w=siner with respect to r, we get…

Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

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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: At a bakery, muffins are made from 4 A.M. to 10 A.M. at a rate modeled by M(t) = 3.85(10 – t)² In(t…

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Q: Let f (t) = et sin 5t

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.