No. 2: X and Y are jointly continuous with joint pdf (CL if 0 Sxs 2,0 Sys2 f(x,y) = {k(3x² + y³) 0, otherwise nd (a) (b) Find the value of k P(|X + Y| > 0.5) () P(:sYs/x = ) (4)

Q: f is a differentiable function. Then (х) dx ef(x) + C el(x}+C f'(x)ex) + C f'(x) + e(x) + C f(x)ex)…

A: topic - integration

Q: Suppose that f (1) = 1, f'(2) = 5, f'(1) = 4, g(1) = 2, g'(1) = 7. Find a. (fo g)'(1) b. (9((x)))…

A:

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

A:

Q: 2x2 - бх + 5 |Let f(x) = Evaluate f' (x) at x = 1. 4x2 + 3x + 10 f'(1) =

A: Given: f(x)=2x2−6x+54x2+3x+10 Quotient rule of differentiation states that ddxfg=f'g-g'fg2

Q: Q:f(x)={xe X = 0 X = 0 test f(x) is continuous at x = 0

A:

Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

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Q: If some function f(x) has a relative extrema at the point (c, f(c)), then f'(c) = 0 True False

A: if we want to fine any fuction has relative extrema then

Q: Let f(x) = 6x/(x³ – 7). Evaluate the following specific values of f': (A) f'(1) = (B) f'(5) =

A: Given the function

Q: 2 Find f such that f'(x) = f(9) = 20. f(x) =O

A: Topic - integration

Q: Let f(z) ==+[=] Find f'(2). x+ [c]*

A:

Q: 23. The graph of a differentiable function ƒ is shown. If h(x) = f(t) dt, which of the following is…

A:

Q: 5 3. Let F(x) /t2 17 dt. Find F'(x)

A: Given:

Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, F(3) = 0 %3D %3D In (1) |-In(\x|) + In(1)x + f(x)

A: Given f"(x) = x-2     ,   x>0   f(1) =0   , f(3)=0

Q: 0.6z Express the function h(x) = Ve' - 3 in the form h(x) = (ƒ o g)(x) where f(x) # x and g(x) ± x…

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Q: Find the linearization L) of the function at a. f(x) = {, 8 = 125

A:

Q: 5. Let X have the pdf f(x) = 5x¹, 0 < x < 1, zero elsewhere. Find the pdf of Y = - 2ln(X).

A: The random variable X has the pdf given below: fx=5x4,   0&lt;x&lt;1 The transformed variable is…

Q: A drug using to treat a particular disease shows 20% failure rate. If we select a sample of 8…

A:

Q: If g(x) = 2 In(xr + 1) and f is a differentiable function of x, which of the following is equivalent…

A: As we know that: The Chain Rule: fgx'=f'gx·g'x The Power Law: ddxxn=nxn-1 Given gx=2lnx+1

Q: 7 Find the most general function F such that F'(): - 5V?.

A:

Q: d) Suppose that f(x) and g(x) are differentiable functions and that h(x) = f(x)g(x). You %3D are…

A:

Q: 8 f'(t) dt 24, what is the value of f(8)? If f(3) 12,f is continuous, and 3

A: Given,

Q: Suppose f is a function for which f'and f" exist. You are given that: S(0) = 1 S'(0) = 5 %3D %3D…

A: here we use the integration by parts see below the answer and calculation

Q: let p(x)=g(f(x)). use the given table to find p'4

A: p(x)=g[f(x)] diff. w. r. to x p'(x)=g'[f(x)] . f'(x)  ..................(1)

Q: x f(x) f'(x) g(x) g'(x) 1 1 1 3 3 4 3 65 1 3 -2 3 4 4-2 -6 51 6 The functions f and g have…

A:

Q: 2x Let f (x) Then the derivative of f is 1 + 4* f'(x) = A(1 + 4*) – Bx(4*) In C where (1 + 4*)D A =…

A:

Q: 2а + bx b) For what values of 'a' and b' the given function f(x) = {12 %3D 2 ах — 3Ь x = 2.

A:

Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

A:

Q: What is the total change of f(x), if f'(x) = 2x - 3, over the interval [1, 3]? -3 O-2 O 2 03

A:

Q: Let f(x)= $ (x- 3)* k- 4k+1 8. Find: %| k=0 a) f'(x)= b) [ƒ(x)dx=

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.