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Q: . Differentiate the function using product rule. f(x) = e*(e* + sin x + x²)

A: Given : fx = exex+sinx+x2

Q: Can you find the stationary points of V and classify each of them by using the 2nd derivative test?

A: Introduction: A real-valued function defined on a closed or bounded interval can have its absolute…

Q: 2. ASSUME f(x) IS CONTINUOUS AND DIFFERENTIABLE ON AN OPEN INTERVAL AS GRAPHED. WHICH OF THESE…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: By using caushy Rieman find the derivative of f(z) =|z| IT 1"

A: We are solving first Que only as per the guidelines. If you want others to be solved kindly post it…

Q: Use Mean value theorem to show that (1+ x)' 2 (1+2x).x21.

A: Mean value theorem: Let f be a continuous function on the closed interval a, b and differentiable on…

Q: [1, 5] th- or f(x) is

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Q: Let Ax) = 2x - 7x +4x. %3D a. On what interval(s) is f'(x) > 0? b. On what interval(s) is fx)…

A: Given: fx=2x3-7x2+4x   The Power law: ddxxn=nxn-1

Q: Runctioy is continuous. eミm show that the xて-2 子(ス1 X メ→2 22 X-2 ス ラ4

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Q: If f is an entire functions then h(z) = e² f(1/2²) is analytic on C\ {0}, and its derivative h'(2) =…

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Q: 5. If f (x) = Vx, g(x) = x + 5 and h(x) = x² – ÷, 1 find the following.

A: Given,            fx=x , gx=x+5  and  hx=x2-1x .

Q: Define. Show that h is continuous at x = 0 but h' (0) does not exist

A: Function is said to be continuous at a point x=a, when the function is defined at a and the limit of…

Q: Sketch a graph of a function f with the following properties. f' 0, for -70 and f''>0, for -50 and…

A: f'<0 and f''<0 for x<-7 f'<0 and f''>0 for -7<x<-5 f'>0 and f''>0 for…

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Q: Find intervals of theta where f is decreasing for r = -4cos(3theta)

A: Approach to solving the question:Let's find the intervals of θ where the function f(θ) is decreasing…

Q: 7) Let f(x) be a function such that f(1) x E [1,6]. Find how small can f (6) possibly be? Explain.…

A: We have

Q: ☺ Find the equation ģ the Lime that is tampent to the curve of fad= (4-32)1 at x =l (Ges fa) =…

A: Find the eqn of tangent to the given curve at x=1

Q: »[32° dx = 3x² A) 6 B) 7 C)8 D) 9 타 10 xdx A) - B) - Suppose F and G are continuous functions with…

A: We have to answer the following...

Q: s=2 caslzt)- Sin S) 7ズ ds Ty pe as eaCkt amw sr usin

A: In this question We want to differentiate s with respect to t.

Q: 2n2 Using the mean-value theorems, show that in sin z w/6

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Q: Only one of the following 5 functions is bijective, Find it Select one: O A. f(x) = 2x - 3 from…

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Q: Let f(x) = cos x - x. Prove that f(x) is continuous on the closed interval [0,2].

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Q: es. there 7. Let f(x) = x4. a) Determine f-¹(x) b) Determine f(f-¹(x)) c) Determine f-¹(ƒ(ƒ˜¹(x)))…

A: According to bartleby guidelines I can answer only first three subparts of a question.  If you want…

Q: Show that f is continuous on (-0,00) sin x if x 4 V

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Q: Determine the signs of f' and f" for each of the intervals. y = f(x) A Bc'D'E'F'G

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Q: By using Ordinary Pifferentiation Equotion (Initral laluel) Compute k coefficrent for f(332,2) by…

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Q: , find: a. the domain and range of f in interval notation For f(x) = /x+17 1. 2 Ans la D, : R, b.…

A: Given: fx=x+172 for finding domain and range of given function, first we draw graph of it as below…

Q: Let f be the function given by ƒ (z)=5 cos² () + In(z + 1) – 3 The derivative of f is given by f'…

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Q: (x-sin x) A- Find lim,-0 1-cos X/

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Q: If f is a continuous function on [a, b], and if f (a) = -2 and ƒ (b) = 2, then there exists a real…

A: Hi, you can find the answer in the handwritten form.  Given f(a)=-2  f(b)= 2

Q: + 7 Find fix) if f"(x) = Nx+1. and f"C0) =1, fcO)=-1, fc0) =7. O cheet metal is to

A: Let's find.

Q: Find the limit

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Q: Let frx) = (x²+2x), and g(4)=(1++) find gof and f.g.

A: Given, fx=x2+2x and gx=1+1x.   The objective is to find g∘f and f∘g.   g∘f is found as follows:…