How many of the following are valid functions? f: R→R, f(x) = e = g: R→ R, g(x) = ln(x² + 1) h : R → R, h(x) = sin()

Q: sin x then

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Q: Determine f g a) f(t) = cos(t), g(t) = t b) f(t)=e¹, g(t) = e' sin(t)

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Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: Show that

A: ∫x f(x) dx=x F(x)-G(x)                                  F'(x)=f(x)G'(x)=F(x)

Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

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Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern…

A: We have to find the differentiations of the give function and find y101.

Q: Q:Findthe domain of the following functions sin 'x (1) s''x (i) [x] 1 (ii)- | x | ,× cos 'x

A: In this question, we need to find the domain of the given functions.

Q: ilf find f'(x). Answer f(x) = 3 sin x 1 + cos a

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Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: If you have any questions let me know in comment box thankyou for your question.

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: Let f(x) = sin(4g(x)). Evaluate f'(x).

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Q: 1-x The equation of the tangent line for y = at (- 2, – 3) is 1+X

A: AS PER GUIDELINES I CAN ATTEMPT ONLY FIRST QUESTION

Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: If f (x) = sin 2x , find all of the stationary points of f (x) on 0<x<2n

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Q: O Find the derivative of the following functions: L 2+3 (a). f(z) = 2-3 (b). f(z) = 2 tan (z) – 7…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…