If function f(x) is not continuous at the value x = a then the derivative of f does not exist at x = a. True False

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

A: We have to find derivative of the function using limit process: fx=x+4 We know the formula of…

Q: Define the derivative of f(x) at x

A: Consider a function f(x) The differentiability of a function:  Let f(x) be a real valued function…

Q: If f(x)=4/x, find the derivative of f(x) at x=2 using the limit definition of the derivative at a…

A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

A:

Q: Find the derivative of f(x) = x2 using the limit definition of derivative.

A: We have given function  f(x)= x2 So using definition of derivative  f'(x) = limh→0fx+h-fxh So,…

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

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: Prove, using the definition of derivative, that if f(x)  = Cps x,then f'(x) =- Sin x

A: Given fx=cos xBy definition of derivativef'x=limh→0 fx+h-fxhfx=cos xThereforef'x=limh→0 cosx+h-cos…

Q: Define the derivative of f(x) at x =a

A: For a function f(x), the derivative is defined as: Now at x=a, the derivative is defined as:

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

A:

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: Find the derivative of f (x) = 2/x using the limit definition.

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Q: Use the definition of a derivative to determine all points for the function f(x) = ((x+|x|)^2)+1 is…

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Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

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Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

A:

Q: Develop a general rule for the nth derivative of xf(x), where f is a differentiable function of x.

A: Given: the function xfx, where f is a differentiable function of x.

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: If the derivative of f is f'(x) = (x – 1)(x + 2), then f is decreasing on (-2, 1) Select one: True…

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Q: A continuous function has a derivative at every point in a given interval. True or False?

A: function is differentiable means that function is continuous as well as smooth at every point of…

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

A: The given function is fx=-5x. Obtain the derivative as follows.

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

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

A: Consider the function, fx=12 The limit definition of the derivatives of a function is given by the…

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

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x + 11 at x = 0

A: To find the derivative of f(x)=x+11 at x=0 Solution: f(x)=x+11 Differentiating both sides w.r.t x we…

Q: Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of…

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Q: Gottfried​ Leibniz, one of the inventors of​ calculus, initially thought that the derivative of​…

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Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we 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: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: Prove, using the definition of derivative, that if f(x) = cos x then f ' (x) = - sin x

A: we have to prove by using the definition of derivative that if f(x)=cosx then f'(x)=-sinx   as we…

Q: If a function is continuous and differentiable then its derivative continuous? True O False

A: A function, y=f(x) is continuous, if there are no holes or jumps in the graph of y=f(x) .

Q: show that the function is derivable and that the derivative is continuous.

A: The objective is to show that the given function is derivable and the derivative is continuous.…

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

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

A: Given that: f(x)=13-x2

Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

Q: What is the limit that will calculate the derivative f'(2) for the function f(x)= x-1

A: solution of the given problem is below...

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: Find the derivative of the function by the limit process. f(x) = x3 − 2x + 1

A: Given function is fx=x3-2x+1. From the definition of derivative, we have f'x=limh→0fx+h-fxh Using…

Q: What is the derivative of f(x) = 1 over x⁵

A: here we use the formula of derivative  ddxxn=nxn-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: Find the derivative of the function by the limit process. f(x) = 5 − 2/3 x

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Q: Find the derivative of the function by the limit process. f(x) = −5x

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Q: Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

A: The definition of the derivative is given by: f'(x)=limh→0f(x+h)-f(x)h⇒f'(0)=limh→0f(h)-f(0)h  ...…