Let f(x)={ 3x , x > 1                { x^3 , x < 1 Sketch the graph of f. Is it possible to find a value k such that f(1)=k,which makes f(x) continuous for all real numbers? Briefly explain.

Q: 5. If f(x)=-3x+5 a) Find f-¹(x). b) Use function composition to prove that they are inverse…

A: a) finding the inverse of f(x)

Q: (1) Find and classify the extremes value of f(x) = 6x* – 4x° over the interval [-2, 2). (2) A…

A: According to Bartleby Q/A guidelines, we only allow solving the first question if multiple questions…

Q: For the function f (x) = 2-x² – x² +x, (a) List the x values where = 0. (b) Are all of these values…

A: Consider the given function, f(x)=2x4-x2+x Find the first derivative of the given function,…

Q: 39,

A: Step 1:To show that the function f(x)=6x−2 defines a one-to-one (injective) function, we need to…

Q: On what interval(s) is the function f(x) = x55x4 + 15 both increasing and concave down? (Enter your…

A:

Q: Write the domain of the function f(x) = arccos(æ), using interval notation, in the space below.

A:

Q: Consider the function f (x) = 3 – |x – 4|| a. Graph the function and verify that f(1) = f(7) b. Note…

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Q: Explain why f(x) satisfies the Intermediate Value Theorem.  f(x)=ex - x3 - 8  Use IVT to show that…

A: Given        f(x)=ex - x3 - 8  To prove that f(x) has a zero on [-2, 1]

Q: Identify the real number at which it is not continuous of the given function

A: To find: The real number where the function is not continuous. Given: The function is fx=xx2-4x+4.…

Q: Consider the real functions f given by f(x)=x2-1. What is the image of 5 under f? Find all pre-imges…

A:

Q: Sketch the graph of f (x) = x 2 + 1 over the interval [-2,2]

A:

Q: Consider the function f(x)= x3 7x² + 2 List the a values of inflection points of the function f. If…

A:

Q: Find the intervals on which f(x) = x(x + 3)(x – 1) is positive by plotting a graph. (Enter your…

A: Given - A function To Find - Interval for f(x)&gt;0

Q: a. Use the definition mtan = lim x→a a. mtan = b. Determine an equation of the tangent line at P. c.…

A:

Q: Determine the intervals on which the function f(x)=e√x is convex upward and convex downward.

A: We find f"(x)

Q: Use Intermediate Value Theorem to check whether f(x) x- 2x -1 has at least one zero between x= -1…

A:

Q: Refer to the function f(x)=[x] determine f(-4.1)

A: Greatest integer function

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A:

Q: Determine if -Graph f:IR-R such that f(x) = x²+1 is surjective -Argue if it is a surjective

A: Step 1: Step 2: Step 3: Step 4:

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.