Problem 1 (Continuous functions). Recall that a function f is said to be continuous at xo if lim f(x) = f(xo). x→x0 ° Show that if f and g are two functions which are continuous at xo, then their sum f + g and product fg are also continuous at xo.

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Q: (4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10…

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Q: 1. Define a function f as follows: | x² + 1 if x 0 4 -3 -2 -1 1 3 The graph of f. (a) Use the limit…

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A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

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A: This question can be solved using the concept of limit and continuity.

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A: We have given that the statement about to the probability density function (pdf) f(x).

Q: The behavior of a function f (x) can be discovered by studying the sign of its derivative f´ (x).…

A: We will be using the information given by you. The behavior of a function f (x) can be discovered by…

Q: 2. Assume all given functions are continuous. If lim (ƒ(x) – g(x)) = 10 and ƒ(5) = −8 x → 5 Find…

A: The objective of the question is to find the value of g(5) given that the limit as x approaches 5 of…

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Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: D. Sketch the graph of a single function f that satisfies all of the following conditions: i) lim…

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Q: Provide complete and clear solution for each question. Work Problem 2 ( +2 x²-x6 x²-100 x+10 B. Find…

A: 8

Q: Find the derivative of the following function using the definition of differentiatio f(x) = -Zx2 +…

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Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx