Compute the x(1) and x(4) for the function x(t) that satisfies the initial problem. x"(t) + 2x'(t) + x(t) = 2 + (t-3) H (t–3) ; where x(0) = 2 , x'(0) = 1 Answer: 2е + 1 x(1) e e4 + 3e3 + 4 x(4) e4

Q: Find an antiderivative F(x) of the function f(x) = 4x² - 6x +5 such that F(1) = 14. F(x)= (Hint:…

A: Solution is given below:

Q: Suppose = f(). (a) Given y(xo) = yo, when does this equation have a unique solution? (b) Make a…

A:

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

A:

Q: Given that g(2)=4 and g'(2)=3, what is the value of h'(2) for the function h(x) = In(g(x))? O 4/3 O…

A:

Q: If h(x)=√ 7 + 6f(x), where f(1)= 7 and f (1)= 2, find h(1). h'(1) = x

A: Given function Where

Q: 2. Identify the iterative function f(x) = x3 – 9x2 – 6 if initial approximation x, = 2.25

A:

Q: 1 f(x) = 1– 3x

A:

Q: Find the third derivative of f(x) = 3√x³-5cosx. 45 O f(x)= 4553 9 O f(x)= - O f(x)= 45 O f(x)= - 9…

A: It can be written as f(x)=3x3/4-5Cos(x)

Q: 5. If f(x) = (x + 1)(x² – 2)³ then f'(x) А. бx (x? — 2)? В. бx (х + 1)(х2 - 2)2 C. 3(x + 1)(x² – 2)²…

A:

Q: (c) J2 +∞ dx 2 x ln² r

A:

Q: 2. (a) Find the linear approximation to f(x) = 60x¹/³ around x = 27. (b) Find the quadratic…

A:

Q: The graph shown below is f(x)=√x+1.If g(x) = f(t)dt, find g '(3). 5 4 3 2 X 5 4 3 2 1 1 2 3 4 5 कृ…

A:

Q: 8. Given the function h(x)=Vx² - 4 +Vx+2, find h(2), h(0), and h(-x).

A: h(x) is given. We have to find h(2), h(0) and h(-x)

Q: If s(0)=−4, s(7)=−5, f(0)=2, and s′(x)=f′(x) on [0,7], determine the value of f(7)? (Do not include…

A: We have to determine the value of f7  given,  s0=-4, s7=-5, f0=2 and s'x=f'x on 0,7 Since, s'x=f'x…

Q: (vi) Suppose that capital expenditure varies with time in such a way that t months from now there…

A:

Q: Given that f(x) = x³ + e-2, and that g(x) = f-1(x), find g' (9). (Hint: f- (9) is a solution to the…

A: The function is fx=x3+ex-2 The function is gx=f-1x

Q: 1. Find the second derivative of f(x) = x5 – 4x + 1. а. 5x3—4 ь. 20х3 с. -20х3— 4

A:

Q: Find the second derivatives, f"(x) of O a) b) f(x) = 2x² + e²² F"(x) = 2e² (4x²+4) F"(x) = 4+e²²(x²…

A: dxndx=nxn-1dexdx=exd dx(a.b)=a.dbdx+b.dadxf(x)=2x2+ex2

Q: If f(x)=2x-3, and g(x) is a function such that g"(0) = 4 and (fg)"(0) = -4, then g'(0) =

A:

Q: Evaluate: J-1)–1) dy 0-my-1-등u-1)" + 즐피 ++ 11-arctan(Y )+c arctan () +c V3(2y+1) O-m-- 1³ + }n² +…

A:

Q: Consider the following functions. (x) = 2 + x, f,(x) = x, f;x) = x² g(x) = c,f,(x) + cof2(x) +…

A: A set of vectors {v1,v2,...,vk } is linearly independent if the vector equation x1v1+x2v2+···+xkvk…

Q: Find the values of the coefficients a, b and c so that the conditions f(0) = 1, f'(0) = -10, and…

A:

Q: Given the functions f(x) = 3+ Vã, g(x) = x² – 3, h(x) 1 - x m(r): I - 3 find the following: 3x + 5'…

A:

Q: Find the derivative of the function. 92-4x + h(x)= e 18x – 4x2 –1 92-4z++ x2 O b. 9x - 8x² – 1…

A:

Q: fa 79 COS nX COs mxdx

A: 2CC=C+C2cos nx cosmx          =cosx(n+m)+cosx(n-m)I=∫02π cosnx cosmx  dxI=12∫02πcosx(n+m)+cosx(n-m)…