Show that (x) = In/x² -1- In /3, f"(x) = 1 and (2) = 0. .2 x* - 1 | Justify your answer.

Q: Find f-1 if f (z) = iz + 1.

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Q: Use mathematical induction to prove that the derivative of f (x) = xn equals nxn−1 whenever n is a…

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Q: Analyze the critical points of f (x) = (2x − x2)ex .

A: fx=2x-x2ex Differentiating with respect to x, we get…

Q: use the second derivative test to find the local exterma of the function  f(x) =x3-9x2-48x+72 on R

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Q: of f(x, y, tion of ve

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Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

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Q: - Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

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Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R

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Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

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Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

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Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

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Q: What is the relative error in estimating the first derivative of f (z) = 25x - 6x2 + 7x- 88 at x-2,…

A: Given equation is f(x) = 25x3 - 6x2 + 7x - 88∴ f′(x) = 75x2 - 12x + 7

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: If I have f^-1(x)= -x+1 how can I find f(x)?

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Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

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Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

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Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x&lt;-11-x2 if -1≤x≤1x2-1  if x&gt;1    To…

Q: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: Find f'(1) for f(x) = In(v6x – 3).

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Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: Approximate the derivative of f(x)-x3+4x2-10x+5=0 at x=3 using the forward, backward and central…

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Q: what is the value of x in second iteration of the function f(x) = sinx - X +5, in the interval of…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

Q: Find the derivative by the limit process. f(x) = 11-x²

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

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Q: Show that x+1/x is increasing on [1,∞]

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: 4. Use the limit definition of derivative to find f'(x) for f(x) = V5x + 1. You will only get credit…

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Q: 2. Is the function given by F(x) = x². 5x + 6 continuous over the interval (-5, 5)? Why or why not?

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

A: Consider the function: fx=13x3-x. Find maxima, minima.   Find f'x by applying axn'=anxn-1.…

Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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