Sæ +1 if x < 1 f (x) = 3 -x if x >1 determine 1→1 lim f(x) determine +1 sketch the gcaph let f be a function defined by

Q: Consider the piecewise defined function Find the values of a and b that make the following function…

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Q: 2/Let g be a function of r, and r- IXI. Let f(X)- g(r). Find grad f(X) for the following functions.…

A: On solving this we will get

Q: A What is the geometric interpretotron d the derivative f'(a )? O Compute im 2-x 人フ1

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Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: Write the functions in a list so that whenever f(x) comes before g(x), ƒ = o(g) or f = 0(g).…

A: The given functions are  ex, xx, lnxx, ex2, 2x, x2, ln2x. We know that f=og iff limx→∞fxgx=0 and…

Q: 3+x; xL1 3- X 14 X 8x 40 x 480 11x -4X; 80LX 280

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Q: 2. (3 marks) be the functions defined by f(x) = x² – 5 and g(x) = vx-5. Find (b) (fog)(- 5) Let f…

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Q: Sketch a function that has all of the following characteristics: * infinite discontinuity at x = −2…

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Q: Let f(x) = x³ 3x - 1.5. Determine whether the Intermediate Value Theorem can be used to show that…

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Q: Determine and explain what value(s) of a make the function f(x) given below continuous. f(x)= ax-1…

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Q: f(x) = 5* – 4 is a 1-1 function. Determine its inverse function f¯'(x).

A: Given: f(x)=5x-4

Q: Use the limit definition of the derivative to answer the following questions about f(x) = 8x².…

A: Given f(x)=8x2 We know that (a+b)2=a2+b2+2ab

Q: Tyive on example of continuous function f: RJR which is not homeomorphis

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Q: 3. Recall that a function of the form f(g(x)) (also written (fog)(x)) is called a composite…

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Q: Draw a graph of a function that satisfies the following p 1) f(x) 0 for x>0 3) f(0) = 0 %3D 4) f is…

A: Given description of function 1) f(x)&lt;0 for x&lt;0 2) f(x)&gt;0 for x&gt;0 3) f(0)=0 4) f is…

Q: For the function given below, which statements concerning Rolle's theorem are true? Select all that…

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Q: Which of the following represent the derivative of the function f at the input x = a? Select all…

A: The definitions of a derivative of a function f at x = a are given below

Q: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) < 0 and f"(x) <…

A: Given problem:- To select graph  with conditions  f'(x) &lt; 0 and F"(x) &lt; 0 for all x…

Q: Consider the function f(x)=x^2-4 / x^2-9. State the domain. State the horizontal and vertical…

A: Note: Multiple subparts are given we are answered with first three parts only.

Q: (a) Explain both mathematically and graphically what makes a function odd or even. b) Use the limit…

A: (a) Suppose fx is a function then mathematically it is said to be odd if  f-x=-fx And graphically, a…