For the function g(x) in part (c), how would you "remove the discontinuity"? In other words, how could you re-define g(x) in order to make it continuous at a = 3? Be sure to write your new function g(x).

Q: Find the x -values (if any) at which f(x) is not continuous, where (x-5

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Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: Use the definition of the derivative to show that the following function is not differentiable at x…

A: Given function, f(x)=9x It can be written as f(x)=9x,       if x≥0-9x,    if x&lt;0

Q: DETERMINE IF THE FOLLOWING FUNCTION IS CONTINUOUS AT THE GIVEN VALUES OF X.  f(x) = 1/x^2 - 9  a.…

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Q: Determine whether the following function is continuous at the given point 1 = 2x+11x f(z) = 2x 13

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

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Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

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Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: - Is the function given by G(x) = Why or why not? continuous at x = 0?

A: We know that function is continuous only if its left hand and right hand limit equal, That is ,…

Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

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Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: Find the value a that will make f(x)={2x^2-7x+3/x-3  if x is not equal to 3…

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Q: Given f(x)=9x^2−7x+4, find f'(x) using the limit definition of the derivative. f'(x)= If you dont…

A: Given function, fx=9x2-7x+4

Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

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Q: Let f be a differentiable function such that f(4) = 3 and f'(x) = -3x + 3. What is the approximation…

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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: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: f(x): at x = 3 X-3 f(x) = at x = 0 f(x)%3D%x6 at x - 0

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Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

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Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: For the f(x) = 1/1-X^2 and g(x)= x^2/1-X^2 A) shows that these functions have the derivative B) what…

A: We need to find relation between f and g.

Q: where is the function f(x)= llxll-2 continuous (or discontinuous)?

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Q: Let f(x)=4x^2-2x-2 find the following: 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4)…

A: We have to find 1) f(x+h)=2) (f(x+h)-f(x))=3) lim h→0 (f(x+h)−f(x))/h4) Find the equation of the…

Q: what is the mathematical condition for the function to be continuous at a certain point c?  is the…

A: A  function is said to be comtiuous at a point x=c , in its domain if the following three conditions…

Q: Give the formula for a function which has vertical asymptotes at x=7 and x = -6 but is otherwise…

A: A function has vertical asymptotes at x=7 and x=-6 but is otherwise continuous.

Q: . Give a function f (x) which tends to 0 as x tends to infinity.

A: We have to find a function which tends to 0 as x tends to infinity.

Q: Consider the function (x)=x²+2x . Using the limit definition of the derivative, show that for any…

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Q: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

A: Authoring guidelines:…

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

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Q: Use the definition of f'(x)=lim/(*+h)-J (x) to find the derivatives of h (а) h0 f(x)=x²-x+2.

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Q: (B) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D

A: Explanation of the answer is as follows

Q: Use the second derivative to determine the intervals on which the given function is concave up and…

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Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 8 lim x→2 x - 2 = -4 It…

A: Consider the given expression limx→2fx+8x-2=-4 Or, -4=limx→2fx+8x-2                            …1…

Q: Determine if the following functions are continuous at the given value of x. Show your solution. 1.…

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Q: Find the value of the constant cc that makes the following function continuous on (−∞,∞)(−∞,∞).…

A: We have been given a piecewise function and we need to determine the value of ‘c’ at which the given…

Q: The distance between the x-intercept of the tangent line to the curve y = and the x-coordinate of…

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Q: Determine if the function is continuous or discontinuous at x = 2. x2 - 1, if x 22 h(x) = 2x-1, if…

A: We have to find

Q: For what values of the constant c is the function f continuous on (-o, )? Show your work. S ex + 4,…

A: Please see the answer below

Q: At what points of R² are the following functions continuous?

A: A function is not continuous at the value of variables when the function does not give a defined…

Q: For f(x) = 2x2 +1, use the definition of the derivative f'(x) = lim (e+h)-}(=) to find f'(x). h0 h O…

A: f(x) is differentiable then  h→0limf(x+h)-f(x)h Here f(x)=2x2+1

Q: For every continuous f:[0,+0) →R _function , if a>0 2fx'f(x*)dx =[ xf(x)dx Demonstrate that this…

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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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: Show whether the following function is continuously differentiable: f(x,y)=x2y2

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Q: Start with g(x) = 3x. Use the limit definition of the derivative to show what g'(x) is.

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Q: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3

Q: If functions ƒ(x) and g(x) are continuous for 0&lt;=x &lt;=1, could ƒ(x)/g(x) possibly be…

A: According to continuity theorem if f(x) and g(x) are continuous on [0,1] then if g(x) ≠ 0 on [0, 1]…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.