If f(x) =. x - 1, then f({-1,0, 1, 2}) =

Q: 1 If f(x) = xī, then f'(x) is equal to %3D

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Q: ax+b x <1 If the function f(x)={ 2x b- x 1< x < 2 is continuous x2 2

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Q: If f(x) t°dt -1 then f'(x) = f'(6) :

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Q: 2. If f(x) = e*+ °, what is f"(x) ? x'+ 5

A: Given that f(x)=ex2+5 find out f11x

Q: If f(x) = e2 In(x²+1), then f'(x) =

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Q: Consider the two functions f(x) = x² + 3x and g(x) = Sx² – 2, x 0

A: Given:                     Evaluate the following

Q: Graph the function f(x) = u₂(x) ln x + u5(x) (ln(10 − x) – In x) -

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Q: A function f(x) = v1 – x² is

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Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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Q: Find the first and second derivatives of the function. h(w) = (w² + 2w + 3)5/2 h'(w) = (5w + 5)(w² +…

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Q: Find for f'(x) | f(x) = x – cos(x) f(x) = e* – 2x - 2

A: To find f'(x).

Q: 10 if f(x)= t +P, then %3D f'(X) = f'(-2)=

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Q: Let h(x)=f(x)g(x). If f(x)=ln(3x2−2x−4) and g(x)=3x−1, what is h′(x)?

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Q: If f(x) = In( 1 + e4x), find f '(0). f '(0) =

A: The objective is to find f'(0).

Q: Find [f(x) + 5g(x)]dx if 6. f(x)dx = 4 and g(x)dx = -5. juo 6. f(x) + 5g(x)]dx -3

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Q: Let f(x)= 2x ; 0<x<1. Find E(3X+5)

A: Given, f(x)=2x   ;0&lt;X&lt;1

Q: Suppose f(1) = 0,f(3) = 1,f'(1) = 2 , and f'(3) = –-3. Evaluate x f"(x) dx. ... A -6 В -8 -12 -10

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Q: Find functions h and g such that (h o g)(x) = (x³3 + 2x – 1). -

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Q: If f(x) = e(n =)*) and g(x) = (In x)², then g(f (x)) is equal to.

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Q: Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x   x^2 - 10x   3x^2   3x^2 + 2x   x^2 + 2x

A: In a polynomial expression, the like terms are the terms with the same variables and exponents.

Q: If f(x) = t° dt then f'(x) = f'(– 6) =

A: SOLUTION-

Q: Let f(x) be a polynomial and g(x) = f '(x) be its derivative. If the degree of (f(x) + f(-x)) is 10,…

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Q: Suppose f(x) = x² In(x). then f"(e) equals

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Q: Let h(x)=f(x)/g(x), where f(x)=ln(3x2 +2x+2) and g(x)=−2x. What is h′(x)?

A: Here we use quotient rule, which is pq'=p'q-pq'q2

Q: If f(x) = (1 + 3 + 5) dt 0, then f"(x) =

A: Given:  f(x)=∫0xt3+3t2+5dt To Find: f''(x)

Q: Find f'(x) for f(x) = e* - 5x.

A: Given : fx =e4x2-5x

Q: Find the domain of the function. g(x) = ln(x - 1)

A: A function is a relation between an input variable and an output variable wherein each input…

Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: If f(x) = tan (3x), then f'(æ): (A) 12 tan (3x) sec2(3x) (B) 4 tan (3x) sec2(3x) (C) 12 tan (3x) (D)…

A: Using chain rule of differentiation

Q: Let f(x)=4x-1, h(x) = -x+ 1. Find (fo h)(2). (fo h)(2)=

A: Given fx=4x-1 and hx=-x+1. To find: f o h2 Solution: We know that, f o hx=fhx Therefore,  f o h2=fh2…

Q: Find a formula for f(n)(x) if f(x) = e' -3x fln)(x):

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Q: If f(x) = 2+|x-3| for all x, then the value of the derivative f'(x) at x= 3 is (A) -1 (B) 0 (С) 1…

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Q: If f(x) = x + 3, g(a) = x- 1 and h(x) = VT, then f(g(h(x)))=

A: Given , f(x)=x4+3 , g(x)=x-1 ,  h(x)=x We need to calculate the value of f(g(h(x))) Now substituting…

Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

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Q: If ɛ ER and the function f(x) = ex – 1+ x² is increasing x E R, show also that e >

A: Since f is increasing hence f'(x) &gt;0 for all x

Q: Find f′(x) and f′(c). Function f(x) = (x3 + 4x)(3x2 + 2x − 5) Value of c = 0

A: Given:fx=x3+4x 3x2+2x-5  To Find: f' (x) and f' (c)

Q: For what value of the constant c is the function f continuous on (-0, ∞)? ( cx2 + 8x if x < 5 f(x)…

A: Given f(x) = cx2+8x   if x&lt;5x3-cx  if x≥5               we find the constant C is the function f…

Q: Find f ◦ g ◦ h where f(x) = |x − 4|, g(x) = 2x , and h(x) = √ x.

A: We have given f(x), g(x), h(x)  We have to find fogoh

Q: If f(x) t3 dt then f'(x) = f'(- 5) =

A: We know that by Second Fundamental Theorem of calculus, if f is continuous on [a,x] and if Then

Q: f(x) = x* – }x' – x + 2x –1 -

A: Given   f(x)= 14x4-23x3-12x2+2x-1has turning point at where the f'(x)=0differntiate f(x) with…

Q: The linear function f(x) = ax + b is a constant function if?

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Q: If f(x) t2 dt then f' (x) = f'(3) =

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Q: If f(x) = In(3x + In(x)), find f'(1). f'(1) = 0

A: Given :f(x)=ln(3x+ln(x))

Q: Find (f-1)' (a)   f(x)  = x3 + 3Sin x  + 2Cos x  , a= 2

A: Given expression: fx=x3+3sinx+2cosx Differentiate the above expression w.r.t 'x'…

Q: Find the domain of the function: h(x) = ln(x - 3)2.

A: Given: hx=lnx-32 By using the property of logarithmic function, the given function can be expressed…

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

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Q: Compute f(x) and f(x) dx for the function f(x) = ∞  ∑…

A: f(x)=∑n=0∞x2n2n !.....(1)This is the well known series of the cosh(x)cosh(x)=∑n=0∞x2n2n !Now as we…

Q: If f(æ) = (x + 1)² – 1 then f(1) – f(0) is equal to:

A: Given f(x)=(x+1)2-1 Now we will find the value of f(1)-f(0) as shown below

Q: 2. If ƒ(x) = x°e*, find f'(x) and f'(1).

A: We have to find f'(x) and f'(1).

Q: Find f'(x), f''(x), and f'"(x). 1 f(x) =

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