Sketch the graph of the function f(x). f(x) is continuous from the right at x = 3, but not from the left.

Q: Use the first and second derivatives of (x)= x - 3x + 1 to determine the intervals on which f is…

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Q: Use the graph to answer the question. Is f continuous at x = 0? %3D -4- -5- 2.

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Q: Sketch the graph of a function f such that f′ > 0 for all x and the rate of change of the…

A: Given A function f with f’>0 and rate of change is decreasing.

Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

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Q: Use the definition of derivative to find f'(x) for f(x) = ax² + 10. f(x+h)– f(x) | f'(x) = lim h0 h

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Q: Match the graph of f, below, with that of its derivative. 3. -3 -2 -1 I 2 3 -3+ 4 ++ -6 -4 -2 4 6 2.…

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Q: The following represents the graph of the derivative f'(x) of a continuous function.

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Q: Let f(x)=x+(1-x)^(1/2). Find the local maximum and minimum values of f using both the first and…

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Q: Find a function f such that f (x) = 2x3 and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A: Key point used: The slope m, of the tangent to f(x) at point h,k, is equal to f'x=h. Given:Eq of…

Q: Find where the function is continuous, but not differentiable..

A: Given,

Q: Let f(x) = 1/x-2. Find f'(x) using the limit definition of the derivative

A: We find f(x+h) first.

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: Find the slope of the secant line between x = -1 and x = 2 on the graph of the function f(x) = -2x +…

A: The given function is fx=-2x3+3. Compute the slope of as follows.

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: Use a graph to explain why. if f is defined at x = a.

A: The given integral is ∫aafxdx Formula used: it is known that the area bounded by the graph of fx and…

Q: Determine where the function f(x) = √ x / x + 1 is increasing and where it is decreasing.

A: fx=xx+1

Q: f(x) at x = - 3 X-3

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Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: At what points are the functions continuous? x + 3 f(x) 2 - et

A: The given function is fx=x+32-ex

Q: Is the function below continuous at x = -5? f(x)=x3−2x2+5x+1

A: We are to simplify

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = x2 / (x +…

A: fx=x2x+x14 The domain is the set of all values of x for which denominator is non-zero. That is,…

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

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Q: Find a function f such that f'(x) = 2x³ and the line 54x + y = 0 is tangent to the graph of f. f(x)…

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Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

Q: Determine whether the function of f(x) is continuous at x = -1 x2 -1 f(x) ={ x +1 X + -1 -2 X = -1

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Q: Sketch the graph of f(x) = x lxl. Then show that f '(0) exists.

A: A function is a relation which maps each value in domain to exactly one value in range.  For a…

Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

Q: Is the function given by f(x)=x^2+3x/2x-1 continuous over its domain?

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Q: Determine where the function f(x) is continuous. f(x) = /2-x

A: We have to determine where th function f(x)=(2-x)^(1/3) is continuous

Q: X- e.

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Q: Let f(x)=x^3-4x^2. Find the points on the graph of f where the tangent line is horizontal.

A: f(x) = x3 - 4x2Horizontal tangent when f'(x) = 0differentiate f(x) with respect to 'x'f'(x) = 3x2 -…

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: What happens to the function f (x) = 1 + as x approaches to zero.

A: The definition of the function gx=x is given by, gx=x for x≥0=-x for x<0 Thus, the left hand…

Q: For the function f, how would you remove the discontinuity? In other words, how would you define…

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Q: Examine whether or not the function (4-x² f (x) =- [4+x if x0 Is continuous at x = 0

A: Check whether limx→0f(x) = limx→0(4-x2) and limx→0(4+x), if both sides are equal then it is…

Q: Find the function f(x) given that f ′ (x) = e x + x and the graph of f passes through the point (0,…

A: Given: f'x=ex+x & Px,y=0,3   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Sketch the graph of the function  f(x) = ln∣x∣ and state its domain.

A: Sketch the graph as shown below:

Q: sketch the graph of a function that is continuous everywhere except at x=3, and is continuous from…

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Q: Use the graph to determine the values of x at which the function is not continuous.   x=

A: Given the graph of the function

Q: Redefine the function f to make it continuous at x = 0. -8x + 36 + x (х — 4) ; x + 0,4 f(x) = 4; x =…

A: Consider the condition for continuity.

Q: Determine if the function is continuous at the given point. 1 f(x) = {* - (x2 – 2 x 0 at x = 0.

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Q: Give the graph or the formula of a function that is continuous but not differentiable at x=0.

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Q: Let f(x) = 2x2 +1. Use the limit definition of the derivative to find f'(x).

A: We can find f'(x) Using following formula

Q: The function f(x) = k is continuous.

A: Given f(x) = k

Q: Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f. f(x)…

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Q: Use the graph of the derivative g'(x) shown below and the terminology: increasing, decreasing, local…

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Q: Select all of the graphs that depict a function which is not differentiable at x=0.

A: Here, we need to select all the graphs that depict a function which is not differentiable at x=0.…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.