|r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = 3 cos(3t)i + 3 sin(3t)j+ tk K(t)

Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: A. cos (T – n1) n=1

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

Q: 1. Find the convolution of f(t) = 3t and g(t) = sin2t?

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Q: Find the value of the summation. cos(Tk) = k=0

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Q: Q2) 1- Find for: y= cos (x)+cos(x*) CoS

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Q: Q2: Use the Newton-Raphson method to find a solution cos(x+ v2) + x+ vz) = 0, for-2sxs-1 accurate to…

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Q: [0,2m] find ao for f(x)=cos 2° 其bO 2n.c0 0 d O x/2

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Q: Given f(2) = | 1+ cos²(1) t2 + 2t – 63 -dt 1+ cos?(t) - At what value of x does the local max of…

A: The local maxima and local minima of a function are the points of where tangent of the function is…

Q: Find f(x).

A: Given,

Q: Topic: Variable Separable and Homogenouse D.E. I need particular solution for 4

A: We have to solve

Q: R4 for g(x) = cos(xx) on [0, 1]

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Q: 6. f(x) cos (4x- 16), when x = 4 (0 in the given function is in degree measure)

A: Given- fx=cos4x-16 To Find- The value of the above expression when x=4 and θ in the degree measure.

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: Solve the second derivative forf (x,y,z) = sin* (x² +y²) a²f ax? x²+y² sin ت )م(. (x² +y²' sin sin…

A: The given function is: f(x,y,z)=esinx2+y2z Differentiating it w.r.t. x: ∂f∂x=esinx2+y2z∂∂xsinx2+y2z…

Q: Q4: (a). Prove that u = 2x(1-y) is harmonic.

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Q: 2- The integration of f x²sin (x³). dx is: (a) cos (x³) + C (b) cos (x³) (e)금 cos (x3) + C (d) 글 cos…

A: According to the bartleby guidelines, for more tan one question asked only the first question should…

Q: 2. Find L{f(t)} if f (t) = = cos 4t + t-1/2 + e5t – sin 3t – 5t – 1.

A: We will use the formulas Lcos at = ss2+a2Leat = 1s-aL(sinat) = as2+a2L(tn) = n!sn+1 Hence we have…

Q: 212 Q3: Find the solution to the equation at Ju(x,c) A- = 0 at x = 0 for all t. B- u(x, t) =0 at x=0…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: ecot x 20. J sin² x(e- cotx) ax is equal to A. ecot x 1 + C ecot x C. -ecot x + C D. –ecot x + C

A: Given problem:-

Q: Given f (t) = t^2 and g ( t) = sin 2t, obtain the convolution (f * g). -ea* -1- cos21) -er -1- cos…

A: Convolution Theorem : f * g t = ∫0tf(u) g(t-u) du   Integration by parts : ∫uv dx = u∫v dx -…

Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

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Q: -(sin³(x) + sin (x³) ) dx A 3sin'x + cos (x³) B 3sin?rcos(x³) + 3xr?cos(x³) © 3sin?x + cos (3x²) D…

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Q: Using FPI, find a critical point of the function: f(x) = x2 – 2e* cos x With an initial guess, xo…

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Q: 1-cosx 4x2 k,x30 Find k so that (x) = is continuous at x-0 1/2 B 1/8 2/5 3/4

A: The function is given as , fx=1-cosx4x2 , x≠0k , x=0 k=?

Q: The derivative with respect to x * 2cos? (x2 + 2) is A. 2sin (x2 + 2) cos (x2 + 2) B. -2sin (x2 + 2)…

A: We will solve the problem.

Q: Let f(x) = cos(x). (a) On [0,2n) solve f(x) = 0. 4.

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Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If an answer does not…

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Q: f(x) = x centered at a -3 is T,(x) = co +q(x+3) + c>(x + 3)? + c3(x + 3)³ + C4(x + 3)*.

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Q: The acceleration ā of a particle at any time t is given by à = e-2 î + 3t ĵ+cos t k , then the…

A: The acceleration of a particle is given by a→=e-2t i^ + 3t j^ +cost k^  v(t) = ∫a(t) dt = ∫(e-2t i^…

Q: Test the ff ODE for exactness and find the general solution of the DE. (2x + 3y) dx + (3x + 4y) dy –…

A: Let's find.

Q: 6. If f(x,y, z) = x³y³ sin (z²)+z³ cos (x³), find an expression for fryz and evaluate it at the…

A: Given f(x,y,z)=x3y3sinz2+z3cosx3 To find: fxyz fxyz at (1,1,π)

Q: 2. If f(x) = 2x – 1 and p(x) = = cos (x). Find x, for 0 < x < 2n, if (f •p)(x) = -2

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Q: find ao for f(x)=cos 2 [0,2m] .a .b IT .C 2n .d 2

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Q: V3 Find the exact values of s in the interval [0,2x) that satisfy the condition, sin s = -

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Q: 1+ x² -L „tanx - for all x €[0,1/2], then f'(x) equals 1+ ex * If f(x) = sec2x A 1+ etanx sec³x B 1+…

A: Given an integral. We need to find f'(x).

Q: f(x) = |x|, −π<x< T 1-(-1)" a. f(x) = 2 Σ=1 sin nx n (-1)"+1 00 b. f(x) = 1 + ² =1 - 2 πT n² (-1)"-1…

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Q: 1 = cos t and f(0) = 4 f(0) + f(0+ 2T) + f(0+ 47) ? If f(t) = cos t what is the exact value of %3D 3…

A: ft=cos t and fθ=-14

Q: Q5) Find f((s) if you know that g(x) = cos(x² – 1). S(x) = 3tan(x*) at vr?

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

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Q: -ツ() The function f(x) is invertible. Find given that f(x) = 5x +4 cos(x).

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Q: The rule cos mx sin nx = cos(m - n)x- cos(m + n)x. T O FO The rule f x" eax dx =x" eax Sxn-1 eax dx…

A: Above questions is solved one by one from top to bottom serial wise.

Q: 2. For g(x) = cos³ (2x - 1), find g' (#). %3D –

A: topic - derivative of a function

Q: Find a root for f(x) = xcos(x) + e* + 2x using the Newton-Raphson second method.

A: The Newton's iteration formula to find the root of function y = f(x) is:  xn+1=xn-f(xn)f'(xn).…

Q: Find y prime for y=(cos(x))^x

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Q: Q2) 1- Find O for: y= cos (x) + cos(x)

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Q: Let f(x) = 3 sin'x - 7 cos(2x), 0 <xS T. Find the interval(s) on which f is increasing. (A) (0, 7)…

A: Recall that, f is increasing on (a,b) if f'(x)&gt;0 in (a,b).

Q: A violin string produces a vibration u(x,t)=a sin(2t-x/ 137). cos(A-t)+b sin(14t-x / 137). cos(E-t)…

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Q: Given x² + 13x + • 40 f(t) = 1+ cos2(x) At what value of t does the local max of f(t) occur? rp- t =

A: Here, the given function is: f(t)=∫0tx2+13x+401+cos2xdx