Solve initial value problem (engineering math) y" + 4y = f(t) y(0) = 2 y' (0)=0 with f(t) = 0 for 0 < t <3 and f(t) = 4 for t> 3

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx &gt; 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

Q: f(x) = 3x² - 2cos(x) find the equation for f'(x).

A: Consider the fucntion

Q: V4 + 3f(x), where f(1) = 7 and f'(1) = 4, 62. If h(x) find h'(1).

A:

Q: 3. (5 points) An elevator moves up and down a building so that its height above the ground (in…

A: Question is solved.

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

A:

Q: Va - 2 find: Va + 2 If f(x) = f'(x) = f'(2) = %3D Submit Question

A:

Q: (x – 3' If f(x) = 4x + 3, find 4

A:

Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

A:

Q: 15) Match the graph with the correction function. (a) (x) = 4' - 5 (b) S(x) = 4' + 5 (c) (1) = 4-X +…

A: (a).    The given function is: f(x)=4x-5

Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.

A: The given function,   f(x)=5xlnx

Q: Find f"(x). f(x) = 6x- 14x-

A: Topic = Derivative

Q: If f(x) = =√(t³3 + 3t² + 6) dt then f"(x) =

A:

Q: Find f'(x) and f'(c). Function f'(x) = f'(c) = f(x) X-7 Value of c c = 1

A:

Q: Find f''(x). f(x) = (x² + 1) * %3D f"(x)=

A: We have to solve

Q: 19 Let ƒ(x) = (19√x – 18) (2³ – 18) (2³ - 2 +23) - X Then the rate of change of the function at x =…

A: The given function is

Q: 2x-3 3x (x-3)2 find the x-value(s) where k'(x) is (are) undefined. If k' (x) : for all x in the…

A:

Q: '5 '5 '5 If f(x) dx = 33 and g(x) dx = 14, find [2f(x) + 3g(x)] dx. %3D

A:

Q: 5-s s² + 4s-5 (A) Find L¹(F(s)}, knowing that: F(s)=- DA

A:

Q: Find f. 4 f'(x) = 1- Ex) = %3D

A: This is a problem related to integral. Based on the given differential equation we will calculate…

Q: If x = e*-Y then is equal to A) B) log z (1+log z)* C)

A: solution:-xy=ex-ytake log both sideslnxy=lnex-yylnx=x-ydifferentiate both sides w.r.t…

Q: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

Q: 1. f(x) = 6x + 15 find f'(x) Answer:

A:

Q: Find f'(x). f(x) = (x² + 1) * f"(x) = %3D

A: Find f''(x)

Q: If f(x) = then f"(x) = = X √ ² ( 2³ + (t³ + 4t² + 5) dt 0 ←

A: Let,Using integration formula So,If  dtPut , dt = F(t)Then So,

Q: 3. If f'(x)= 3x² 2 and f(1) = 4, find f(e).

A: To find f(x) from f'(x) we integrate it C=integrating constant