Suppose f(x) is the function such that for a > 0 we have f(x) = (e" – 1) In(x) and for x < 0 we have f(x) = |x| cos x. Which one(s) holds for f(x) if f(0) = 0?

Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: • Find f (x) of f(x)=by using the definition of the х-1 derivative. • 1- Find if y=3t-4 and t = Vx +…

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Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0]. If we use…

A: For finding a zero of a function f, the secant method is defined by the recurrence relation.…

Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

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Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: cos x 13. lim x→(T/2)* 1 – sin x

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

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Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: Find the critical points of f (x) = 2 cos 3x + 3 cos 2x in [0, 2π]. Check your answer against a…

A: Given: f(x)=2 cos(3x)+3 cos(2x), 0, 2π

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

A: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)f() <0, f(x) has a root in [0, 1]. If we use…

A: The given function is                    f(x)=cos x-3x+1 It is known that f(x) has a root in 0, π2.…

Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given :             cosh(3x2y) = x + ln(exy + 1)   To find :            ∂y∂x

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Let f (x) =x. cos(x2). what is the correct result of the derivative of f with respect to x? A…

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Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

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Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

Q: Solve for x in the interval 0 < x < 2n. log (sin (x)) – log (cos (x)) = 0 a) x = 5,

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Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)ƒ () <0. f(x) has a root [] If we use secant…

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Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: Use the Intermediate Value Theorem to show that 2x – 3 - if – 3 0 has a zero on the interval [-2,…

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

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Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2). O…

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Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

Q: If f(x) = x[5 sin (In x) + 2 cos (In x)], find the first derivative f'(x). A. x[3 sin (In x) + 7 cos…

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Q: The equation of the tangent line for the graph of F(x)= Ln (f+4)df at x=2 is O y-Ln(68)(x-2) O…

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Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

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Q: Consider the function g defined by 1 g(x, y) = cos (7x/) - CoS log3(x – y)

A: Given problem:-

Q: The derivative of the function f is given by ƒ'(x): = e¯* cos(x²), for all real numbers x. What is…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0, f(x) has a root in [0]. If we use…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Q: If f(x) = A B tanx 1+e 1+1² 1+e¹ In (secx) √ 1+tan²x 1+ e tanx sec 3x tanx -dt, then f'(x) equals

A: solution:-f(x)=∫0tanx1+t21+etdtApplying leibniz integral…

Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

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Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…

Q: Let f (x) = x sin x and g(x) = x cos x. (a) Show that f ,(x) = g(x) + sin x and g ,(x) = −f (x) +…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.