Determine whether the following function has a hole. If so, find the hole. x² – 3x g(x) = x' +x-12 Hole? (circle one) yes no If yes, Hole:

Q: Find the derivative of the function g(x) = 3arccos(x/2)

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Q: Differentiate the following function.   y =ln (x2 + 1) / (2x + 3)

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Q: For what values of æ does the function f (x) = 12x – x³ have a horizontal tangent line? Select all…

A: We need to find the horizontal tangent line for: f(x) = 12x-x3

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

A: We find the limit of the ratio of the two functions

Q: Find the Arc lenght of the graph of the function f(x)=(4/5)x^5/4 on (0,4)

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Q: For each of the functions below, select the reason why it is not differentiable at =0.

A: We have to find out the reason for not differentiability.

Q: 1. Find the function whose derivative is XV X xª – 1

A: We need to find a function whose derivative is 1xx4-1

Q: Consider the following function h(x) = -3r – 5x* + 20z³ + 60x. Find the point on the graph of h(x)…

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Q: Differentiate the following function.   y =  ln -2x + 1

A: Given function is y=ln-2x+1. To differentiate the given function. Solution: Chain rule of…

Q: Differentiate and simplify this function g (y) = y3 / ln(2y)

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Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

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Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: Sketch the graph of the function y=ln(x+1)−1.

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Q: Find all possible functions with the given derivative. y = 5x -7x

A: y'=5x2-7x

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

A: Concept: Trigonometry is used in finding distance and angles, there are six trigonometric ratios and…

Q: Find a formula for the nth derivative y^n of the function y=(x+5)^1/2

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Q: For what values of æ does the function f (x) = 12x – æ³ have a horizontal tangent line? Select all…

A: The given function is fx=12x-x3

Q: In the given question , find all functions f having the indicated property? The tangent to the graph…

A: Explanation: Given a function f(x) and point of tangency (x,y). Also given that, the tangent line…

Q: Differentiate the following function.   y = (ex + 1) / (x - 1)

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Q: Which of the following functions grow faster than x2 as x→ ∞?Which grow at the same rate as x2?…

A: Let, fx=x2gx=1.1x Now, If limx→∞f(x)g(x)=1     →both function are growing with the same…

Q: Determine for what values of x the function f(x) = 32 ln(x) − x^2 + 6x − 5 has a tangent line with…

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Q: 1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step…

A: Topic:- function and it's Derivatives

Q: 2. Find the derivative of the following functions: (a). f(x) = x + 4x-2 + 6e" [1 Mark]

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Q: Choose the correct graph of the function (in blue) and its derivative (in red) below. O B. c.

A: We will use the fact that where the function has maxima and minima derivative graph will show value…

Q: Determine the equation of the tangent line to the graph of y = f'(x) at the point where x = 1 if…

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Q: y = cosº (4x)

A: Given: y=cos94x As we know that: The Power Rule: ddxxn=nxn-1 The Chain Rule: fgx'=f'gx·g'x

Q: Find the anti-derivative of the function and evaluate. g(x)=2x g(0)=7

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Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

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Q: find an antiderivative for each function. Do as manyas you can mentally. Check your answers by…

A: If -x-2 has derivative 2x-3 so any equation of the form -x-2+ C is an anti-derivative. We have,…

Q: For the following function, find the first derivative, do a sign graph of the frst derivative, and…

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Q: find the function with the given derivative whosegraph passes through the point P.39. ƒ′(x) = 2x -…

A: We have to find the function for the given derivative passes through the point P: f'x=2x-1, P0, 0…

Q: If f and g are the functions whose graphs are shown, let  u(x) = f(g(x)),   v(x) = g(f(x)), and…

A: The given graphs of f and g are

Q: find all possible functions with the givenderivative. y' = x2

A: Given function  y'=x2 That is dydx=x2dy=x2dx

Q: Suppose this graph represents the 1st derivative function, f'(x). At what value(s) of x does Ax)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: help!

A: Given function is

Q: find an antiderivative for each function. Do as manyas you can mentally. Check your answers by…

A: We know that the antiderivative of a function can be derived upon integrating the function with…

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx +5 at x-2? %3!

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Q: O For what value of x does the function f (x) = 4x2 – x +1 have a horizontal tangent?

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Q: f(x) = loga x

A: ddxlogax

Q: Differentiate the function below y = ln ( ( etan x √(x2 +1) )  /  (x-3)5)

A: We first simplify the given function.  y=lnetanxx2+1(x-3)5y=ln(etanx)+lnx2+1-ln(x-3)5  [addition and…

Q: Q4. Find the slope of the tangent line to the function f(x)= e* +3; x+2 at x=4 5x-10

A: Given : fx = ex5x-10

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

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Q: Find the following derivative 1 g(x) = 2* · (x² + 1)

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Q: f(x) = In(x² + 1)

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Q: Find all possible functions with the given derivative. f'(x) = x* f(x) =O

A: To find out the function.

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

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Q: What is the first derivative with respect to x of the function g(x)= 4/9 * О 4/9 O 4 O 12

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Q: Which of the following functions grow faster than x2 as x→ ∞?Which grow at the same rate as x2?…

A: Let f(x) and g(x) are two functions. 1) If limx→∞fxgx=∞ then f(x) grows faster than g(x) as x→∞. 2)…