Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct answer.] T(0) = (i+j+k) and N(0) = =√(i-j) T(0) = (i-j+k) and N(0) = √(i+j) OT(0) = (i-j+k) and N(0) =√(1-1) j) T(0) = (i+j+k) and N(0)=√(-i+j)

Q: y''' -3y'' + 3y' -y = (e^x)(x+1) find the general solutions of this diff eq

A: Given differential equation is y'''−3y''+3y'−y=exx+1 Write the auxiliary equation  m3−3m2+3m−1=0…

Q: f"(x) = 4x – 2 and f'(-3) = -3 and f(-3) = –6. Find f' (x) = %3D and find f(4) :

A: f''(x)=4x-2 f'(-3)=-3 , f(-3)=-6

Q: Find f. r'(x) = Vx(3 + 10x), (1) = 11 (x)

A:

Q: If the function f(x) is defined as f(x) = = (4-2√√x)² √x -,x>0 Then, what is the value of ƒ'(16) = ?

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Q: find y as a function of x if: y'''-13y''+42y'=60e^x, y(0)=11, y'(0)=24, y''(0)=21

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Q: 2 For the function f(x)=√x² +4, find f''(x). Then find f''(0) and f''(9).

A: Given query is to find indicated derivative.

Q: Find y as a function of a if y(1) = 8, y'(1) = 6. y = x²y" + 3xy' - 35y = 0,

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Q: f"(x) = 2x – 4 and f'(-1) = -1 and f(-1) = -3. Find f'(x) = and find f(4) = %3D

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Q: Decide whether 3f”(x)+20f’(x)-7f(x)=0 for f(x)=ae^r 1^x + be^r 2^x. Substitute your values for r1…

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Q: Find f.  f''(t)=sint+cost,    f(0)=1,    f'(0)=2f′′(t)=sint+cost,    f(0)=1,    f′(0)=2   f(t)=

A: Given as f"x=sin t + cos t integrate both sides then f'x=cos t-sin t+CPut f'0=2Thus2=1+C⇒C=1 Thus…

Q: Find the quadratic function such that f(4) = - 26, f '(4) = -19 and f ''(4) = -6.

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Q: Find f such that f'(x) = f(x)= f(16) = 21.

A: Topic:- application of integration

Q: For f(x) = x² x² Saldainia x a. f(2)=[ b. f' (2) = [ c. f(3) = f(2)= 4. find f(2). f'(2). and f(3)…

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Q: Find the x-coordinate(s) for the point(s) of inflection f(x) =(3x-2) - 4(2x 1)

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Q: Find f. f"(x) = -2 + 18x – 12x2, f(0) = 4, f'(0) = 18 f(x) =

A: The objective is to find f(x).

Q: y'-2ty = t

A:

Q: Find y as a function of x if y(1) = -4, y'(1) = -7. y = x²y" - 2xy' - 40y = 0,

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Q: f(x) = /7x + 8, find f'(x).

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Q: If F(x) = √x + 1, find F (t^2 − 1)

A: We have given  Fx=x+1 We have to find Ft2-1 Then, Ft2-1=t2-1+1