Prove that Define functions f(x) and g(x) as follows: I 2 f(x) = ²/7/17 √ ² e-ºdt, S 0 L {f(t)} 2 g(x) = 7²/17 *° e² √T g(s/2) s2/4 S e-t² dt

Q: a) Differentiate the function Q(p) = -2³√/p³ (²-P). b) Hence or otherwise, determine Q'(1).

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Q: Find function g if | g'(x) = 30 cscxcotx. 20 /1-x² 2.

A: Given that,  g'(x) = x53 - x75x2030 + 21 - x2 - cosec x cot x To find the g(x)    Now,  g'(x) =…

Q: Suppose that f(x) is a function with f(155)=70 and f′(155)=1. Estimate f(157

A: topic -  line and differentiation

Q: iff.g,h becontinuous functions on [0,a]such that and sh(x)-4h(a - x)=5, then provw that…

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Q: Calculate Rs for f(x) = 6 - x over ver [3,5]. R8 IE

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Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: (x)= 3sin(2x +1) iii. In x y= - iv. 2

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Q: Find f such that f'(x) = f(x)= 9 √x f(1) = 32.

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Q: For the relation x²y - y² = 1 - x, find its first derivative at the point where x = 1 and y = 0.…

A: For the relation , to find its first derivative at the point where  .

Q: 2) Find the derivative of the following function 1² +5 1² – 5 (a). f(x) = (b). f(x) = 2 tan '(x) –…

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Q: 1. Let F(t) = sint for t€ [-T/2, π/2]. Calculate (a) f/² xdF(x). (b) 2 xdF(x).

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Q: Find

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Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: Find ao of the function f(x) 1-Cosx f(x) =

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Q: i) Consider f(x) = x² – 3x . a. Find f(2) . b. Determine f'(x). c. Find f'(2) .

A: Hi, As given are multiple questions, according to the Bartleby rules we are supposed to do 3 sub…

Q: Let y be a function such that y(1) = -9/4 , where Y(s) = L {y (t)}. If it is known that:…

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Q: x2 1)Calculate the derivative using FTC(1): g(x) = ʃ  (t5 − 9t3 )dt…

A: 1) to find the derivative of the integral using FTC(1)

Q: Find the value for X, such that the function f(x, y) = x ln(x+y) satisfies f X fa- fy+Xfay - fax -…

A: Consider the function fx, y=xlnx+y. To find the value for λ such that the function fx, y=xlnx+y…

Q: Determine the domain for each of the following functions and sketch the domain. (a) f(x, y) = /T– g²…

A: Set of all possible inputs for the function is called the Domain a the function.

Q: functions identical?

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Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]

Q: Given g(z) = In(5z+), the derivative g (z) is. %3D O 42 O 5z +z O 20z +1 O 20z +1 5z4 +z 5z +I 20z+1

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