Sketch the graph of a function that satisfies all of the given conditions. f'(0) = f'(4) = 0, f'(x) = 1 if x < -1, f'(x) > 0 if 0 4, lim f'(x) = ∞, lim f'(x) = -∞, x→2+ f"(x) > 0 if – 1< x < 2 or 2 < x < 4, f"(x) < 0 if > 4

Q: find the limit as x approaches 1 from the right of  ln(x^9-1)-ln(x^7-1) using L'Hospitals' rule

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

A: Given, f(x)=11-x2

Q: Find the derivative of the function by the limit process. 9. f(x) = %3D f'(x) =

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Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A: Given that the function is        f(x) = x e-x^2

Q: The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a…

A: Given information:Tyhe given function is cosh(x).

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: et +ex -x²-2 Lim- x-0 sin²x-x²

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Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: limit x approaches 0, (xcot2x)

A: Limit x-&gt; 0 ( x/tanx ) =1Calculating the limit of the given expression using this result:

Q: Calculate limh→0 f(x+h)-f(x) for f (x) = /2x+3. %3D h f(x+h)- f(x) /2x+3 limh0 h -2(2x+3)…

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Q: lim as x--&gt;0  of (x+1-cosx)/x

A: The given limit of the function:

Q: The first derivative of y=cos(tan(x2-7x+1)) is.. 1. O -[sin(tan(x²-7x+1))][sec²(2x-7)] 2. O…

A: Find the derivative of y=costanx2-7x+1

Q: 1. Find the derivative of f(x) = 2. at x = 0 using the definition of the derivative as a limit. Va +…

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Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Find the derivative of the function by the limit process. f(x) = 6/x^2

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Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 8

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Q: Find the derivative of f(x) = √x^2 + 1 at a = 2, using the limit definition (i.e. first principles)

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Q: Find the derivative by the limit process. f(x) = 14-x²

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Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: Find the derivative of g(x)= (x+1)/(x+2) using th limit definition.

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Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of…

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

Q: Find the derivative of the function by the limit process.

A: Given: fx=x3-12x

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

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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: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: find the derivative of the function f(x)=x^2 -2x using the definition of the derivative (a process…

A: Explanation of the answer is as follows

Q: Find the derivative of the function by the limit process. f(x) = x3 − 12x

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Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given,          The function is fx=7x-9.

Q: Compute f'(3) using the limit definition of derivative if f

A: Given: f(x)=6x2f'(3)

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: Find the derivative of the function f(x)=1/x using limit definition derivative

A: According to the given information it is required to calculate the derivative of the function using…

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: find any locl maximum and locl minimum values by using first derivative: f(x)-x-2x

A: Given :           f(x) = x4 - 2x2

Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…

Q: Find the derivative of the function by the limit process. f(x) = 7

A: The given function f(x)=7. The derivative of the limit  for the function f(x) is defined by So, to…

Q: Find the derivative of the function by the limit process. f(x) = 31 f'(x) =

A: The given function is fx=31.

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

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Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: To find the slope of the tangent we need dy/dx at x=2 So the slope of the tangent is 4

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: The coordinates of the critical point according to the criterion of the first derivative of the…

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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: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

Q: limit as x approaches infinity of (-1)x+1

A: Apply the limit.

Q: generate a continuous and differentiable function that is decreasing at -6, has a local minimum at…

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