Compute the value of the limit below by relating the limit to the definition of a derivative of a particular function f(x) at a particular value of x = a. x21 + 1 lim X-1 X+1

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

Q: Use the definition of the derviative to compute the derivative of f(x) = at the specific х 3.…

A: We will obtain the answer in two steps: We will simplify the difference quotient We will then…

Q: Let (7z 2x2 for I<0, 8z2 + 7x for r20. f(1) = According to the definition of the derivative, to…

A: Given : Derivative any function is as follows let   f(x)= xm

Q: Use the limit definition of the derivative function to find 4 x*]. dz Which of the following sets up…

A: We need to evaluate an equivalent expression of the following derivative using limit definition…

Q: Approximate the given limit numerically and verify your answer graphically. Round your answer to…

A: Given limit, limx→0+xlnx+x2

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Let f(x) = Vx. Use the definition of derivatives as limit of difference quotient to show that f'(x)…

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Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

A: f(x)=x3, a=-2

Q: Suppose f(x) can find a derivative at x = a, then the following limit is equal to f'(a) is ( ). (A)…

A: Since :                 f(x) can find a derivative at x=a, then the limit equal to f'(a) is :…

Q: Find the limit by interpreting the expression as an appropriate derivative. In(e + Ax) – 7 (а) lim…

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Q: Can f(x) approach a limit as x ➔ c if f(c) is undefined? If so, give an example.

A: Yes .This statement f(x) approach a limit as x ➔ c if f(c) is undefined is correct. We will see one…

Q: Use the definition of the derviative to compute the derivative of f(x) = at the 2. Evaluate the…

A: Calculate the value for f(x) at x = (2 + h) and x = 2. Simplify the numerator.…

Q: 1. If f(r) = x – 2, compute the following: a) f(1) = b) f(1+h} = c) f(1+h) – f(1) Bring your answer…

A: 2a) Given: The function is f(x)=x2-2   To determine: f'(1)=limh→0f(1+h)-f(1)h

Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: Given f(x) = 6 x + 1, find f'(x) using the limit definition of the derivative. f' (x)3D

A: Given, fx=6x+1 We have to find f'x using the limit definition of derivative.

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A: To obtain the value of limx→03x-fx4x-fx, substitute 0 for x and 1 for f(0) in the expression, and…

Q: Let g(x)=(1)/(1+x). Use the limit definition of the derivative to find g'(1). Use the formula…

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Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

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Q: Use the limit definition of the derivative function to find 4 x2]. dz Which of the following sets up…

A: The objective is to use the definition of limit to find the derivative.

Q: Evaluate the limit: sinx lim x→0 e4x – 1

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Q: evaluate the limit  limit as x approaches infinity of x+cos(x)/ x+1

A: To find,

Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: Prove that a function f is continuous at a limit point p iff the limit as x goes to p is f(p).

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Q: According to the definition of the derivative, to compute f'(0), we need to compute the left-hand…

A: Find the derivative of f(x) at x=0

Q: In each case use the limit definition to compute f'(0), and then find the equation of the tangent…

A: Given: a fx=xex   b fx=x2ex

Q: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: Determine the value of the following limit. sinh(x) = x lim - x3

A: Given that limx-&gt;0 sinhx-xx3

Q: if f(z) = V3+ 3z, find f'(3), using the definition of derivative f'(3) is the limit as z+ of the…

A: Given query is to find the derivative using definition.

Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

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Q: When using the definition of limit to prove that L is the limit of f(x) as x approaches c, you find…

A: The ε-δ definition of a limit is an algebraically precise formulation of evaluating the limit of a…

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

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Q: Given f(x) = 3√x, find f'(x) using the limit definition of the derivative, f(x +h)-f(x) f'(x) = lim…

A: Given the expression for the derivative of the function is: f'x=limh→0fx+h-fxh And fx=3x

Q: Use the definition of the derviative to compute the derivative of f(x) at the specific point r = 2.…

A: Topic : limit

Q: The following limit represents the derivative of some function f at sor a. (1+h)" – 1 lim h >0

A: Limit derivative formula is  limh-&gt;0f(a+h)-f(a)h from the given limit we can see that f(x)=1…

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

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Q: Using the limit definition of a derivative, find the derivative of f(r) = r² - r. Show that this…

A: Given,           f(x)=x2-x

Q: Find the limit by interpreting the expression as an appropriate derivative. In (e10 + Дӕ) — 10 (а)…

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Q: Let f(x) = VT. Use the definition of derivatives as limit of difference quotient to show that…

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Q: The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = =…

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Q: Let -2x² + 6x - 3 for x 0. According to the alternate form of the definition of the derivative, to…

A: We will use properties derivative.

Q: Use a derivative (not L'Hospital's Rule) to evaluate (2 + h)4 – 16 lim h Enter the limit in the…

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Q: Let f(x)={−4x+3   x≠4               {3       x=4. What is f(4)? If f(4) does not exist, type: 99999…

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Q: Given f(x) = 5x³ + 7x + 7, write a limit representing the derivative of f(x) at x = −2. Provide your…

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Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: 9 Given f(x): = =, find f'(x) using the limit definition of the derivative. x f'(x)=

A: The given function is fx=9x

Q: Does the existence and value of the limit of a function f(x) as x approaches a ever depend on what…

A: Yes, existence and value of the limit of a function f(x) as x approaches a depends on what happens…

Q: Find the limit by interpreting the expression as an appropriate derivative. e2x lim- 1 i X0

A: As we already know that, dydxx=a=limh→0f(a+h)-f(a)h

Q: 1. Find the points at which f is discontinuous. At each of these points, state the type of…

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