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, f"(x) > 0 if –1 4 1-2

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: limit x approaches 0, (xcot2x)

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

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

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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: Use the limit definition of the derivative (as demonstrated on the left) to compute the exact…

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A: To find the equation of the tangent line to the graph of: y=f(x)=ln(-x) at x=x0=-e4 The equation of…

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

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A: Solve g'(x)=0 to obtain the critical points. Then evaluate g'' at those critical points. If it is…

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Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

A: We need to find the limits of the given expressions by using the L.Hopital rule. For (1),

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Q: Find the limit: limx→0 (sinx−x)/x^3

A: Please see the answer in Step 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: A continuous function has a derivative at every point in a given interval. True or False?

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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: 3. y = at point (0, -) X-3

A: Topic = Derivative

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

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

A: Given :           f(x) = x4 - 2x2

Q: Evaluate the limit. (If an answer does not exist, enter DNE.) y= lim (10x)$sin(7x) X0+ %3= Work must…

A: Now we will find the value of the given limit.  We know,   sinx = 1/ cosecx

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 first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

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Q: Limit x approaches to minus infinity under root 5-x

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Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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