QI Find f'(2) for (x³ – x)(x² + 2)(x² + x - 1) x + 2 f(x) = 587/3 O 379/7 585/4 O 676/5 O 699/7 384/9

Q: x²-x+1 Find the derivative of the function f(x)=- o (2x)-(x²-x+1)xr-1/2 3/2+. 1/2-x-3/2 O…

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Q: x³+3x f(x) = 2-4x+3

A: Given that fx=x3+3xx2-4x+3   Quotient rule for differentiation. ddxuv=v·ddxu-uddxvv2 Here,  u=x3+3x,…

Q: Perform a first derivative test on the function f(x) = x/64 - x ;[-8,8]. a. Locate the critical…

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Q: Evaluate the second derivative of the given function for the given value of x. 2 3 4 y 3x --,X%= -8…

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Q: First Derivative Error f'(x) =: 2h -f(x)+8f(x,)-8f(x,-) + f(x,-2) 12h f'(x) = Second Derivative…

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Q: Differentiate the function. f(x) = ln  7   x f '(x) =

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Q: lim x-->0 (1+sinx)^(1/x)

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Q: *Introduction to Derivatives (x²+2x-3 Using the 3 conditions, show that f(x) = 4 if x#1 is both…

A: Differential function is always contious bt Converse is not true

Q: b) Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

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Q: Tangent line of a graph of f(x)=x(b^x)at x=1 is equal to the tangent line for the graph of…

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Q: lim x→0 (sin3x sin5x/x2)

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Q: f(x) = (- 3x_1 3

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Q: Find the limit

A: We know that cos0=1  For x=0-, cosx will be less than 1.  So, |cosx-1|= -(cosx-1)= 1-cosx for x=0-…

Q: y = 1.2889x3 - 358.53x2 + 48536x - 34188 What is the second derivative, what is the point of…

A: we have been given an equation  y=1.2889x3-358.53x2+48536x-34188 to find the inflection point we…

Q: Perform a first derivative test on the function f(x) = x/9 -x;(-3,3]. a. Locate the critical points…

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Q: sin(3 – x) lim с2 — 5х + 6 x→2 x2 – 5x + 6

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Q: Perform a first derivative test on the function f(x) = x/25 - x;(-5,5]. a. Locate the critical…

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Q: sechx+cshx b) prove that e2x cshx-sechx

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Q: *Introduction to Derivatives (x²+2x-3 if x#1 (4 Using the 3 conditions, show that f(x) = is both…

A: Three conditions of continuity of a function f(x) at x=a: (i) f(a) is defined. (ii) limx→a f(x)…

Q: he local maximum and minimum values of the function f(x)=-x-(25/x). using the Second Derivative

A: Given function is fx=−x−25x To find the local maximum and local minimum of the function using the…

Q: Perform a first derivative test on the function f(x) = x/100 - x² ;[- 10,10]. a. Locate the critical…

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Q: 6 - 5x + x2 Find any local extrema (maximums and minimums) of f(x) = Identify the x value at which…

A: Ans:   we will find the local extrema (maximums and minimums) of the given function using first and…

Q: cos2x – sin2x cos2x For -dr =-F(x)+ C• What is F(x)? cosx - sinx A sinx – cosx) - B 2 sinx + -cos'x+…

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Q: QI/Solve by mean value theorem 1- F(x)=x² In the interval [1,-1] 2-F(x)=coshx In the interval [-1,3]…

A: 1) F(x)=x2. According to mean value theorem. F'(c)=-12-(1)2-1-12c=0c=0 Since, c∈1,-1. Hence , Mean…

Q: QI Find f'(x) for 1+ sec1(x) 1- csc-1(x) csc (x) + sec '(x) V(-1)(csc 1(x) - 1)* csc (x) + sec '(x)…

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Q: refertoihe Furction (f. thXX f(x)%=X+10 D=DX hox-2xt7 Dox²+3X+n x2+3X+17 Oe-X2-x+3 40-X2-X十9 2.

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Q: Differentiate f and find the domain of f. (Enter the domain in interval notation.) f(x) = ln(x2 −…

A: Given function is - f(x) = ln(x2 − 18x)

Q: Find the limit

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Q: h(x) = 4/((x-1)^2) Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in…

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Q: f f(x) = x²√Inx² x . find the derivative of this function f'(x) 1-In x² x²√√In x² A. f'(x) = B.…

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Q: The derivative of the function f(x) = -822 - 12z + 25 by definition of derivatives f(z + h) - f(x)…

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Q: (x² +8) cotx 2 - cos x csc x Find f' (x) when f (x) = 2x cot x – (x² + 8) csc²x A. f' (x) = csc²x 4x…

A: As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Product rule: f·g'=f'·g+f·g' The…

Q: 5 - x2 + 2x – 3 = 0

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Q: QI/Solve by mean value theorem 1- F(x)=x² In the interval [1,-1] 2-F(x)=coshx In the interval [-1,3]…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Derivatives: using (4 step rule). 4. f(x)=sin3xcos3x 5. f(x)= x² cos(x² +1)

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Q: cos2r – sin2x cos2x For -dr=-F(x)+C What is F(x)? cosx – sinx 3 2 sinx + -cos'x+ cosx+ =sin³x 3 3 2…

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Q: lim x -> 0    ln(1+x)-x / 1-cosx   = ?

A: To find lim x -> 0    ln(1+x)-x / 1-cosx   = ?

Q: lim X-3 Sinx X->o

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Q: First and second derivatives Find ƒ′(x) and ƒ″(x).

A: Given, fx=x2-7xx+1

Q: Limit Sin 1/x x -0

A: Answer is mentioned below

Q: g(x)=(2x-x3) h(x)=(8x+5) f(x)=(2x-x3)(8x-5) Find g1(X) and find h1(X) Use product rule to find…

A: Given functions are:

Q: -9) √(x+2)]2

A: The function given is , fx=x2-9x+22. To find the derivative of the function, Apply the product rule,…

Q: Find the local extreme values of f(x) = 1 + 3x2 − 2x3 using the Second Derivative Test.

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Q: The rate of growth of the profit ( in millions ) of an invention is approximated by P ' ( x ) = xe…

A: Given P'x=xe-x2. Thus calculate profit function in millions Px:  Px=∫xe-x2dx       =-12∫e-x2d-x2…

Q: Using "Numerical Differentiation (Backward Finite Difference)" Problem Solving f(x) = 2cos (3x-2)…

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Q: Use differential calculus to find the exact intervals where the function is increasing or…

A: Given that: f(x)=x4-4x3-8x2+5

Q: Perform a first derivative test on the function f(x) = x 16-x:(-4,4). a. Locate the critical points…

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Q: QI Find f'(x) for 1+ sec-(x) S(x) 1- csc-1(x)

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Q: Using product rule to find f’(1) in f(x)=4x^4(e^x)

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Q: QI Find f'(x) for 1+ sec1(x) (x) = 1- csc-1(x) -csc (x) + sec (x) csc '(x) + sec '(x) V(x? - 1)(1-…

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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.