Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove that g(x) = −f(x) for all x ∈ R. b) Suppose neither limx→0 f(x) nor limx→0 g(x) exists. Show that limx→0 [f(x)g(x)] may exist.

Q: 1 lim x x→0

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Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

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…

A:

Q: Suppose f: (0, ∞o) → (0, ∞o) is a continuous function. True or false: lim √f(x) = = /lim f(x). 2-5…

A: We have to find whether given statement is true or not?

Q: q). State the equations of the horizontal asymptotes. r). State the equations of the vertical…

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Q: Let f be defined in an open interval that contains a=3 and assume that all x,…

A: f be defined in an open interval that contains a=3 and assume that all x,2x+6≤f(x)≤x2-4x+15

Q: If f(x+ y)= f(x)f (y) for all x, y eR and f (x)=1+g(x)G(x), where lim g (x)=0 and lim G (x)…

A: The problem has been solved in detail in the next step.

Q: Let f be a function sati sfying f(x+y)= f(x)f(y)-/4-f(y) for all x, y e R. and lim f(x)= 4. discuss…

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Q: 6. Consider a function f with the following property: if g is any function for which lim g(x) does…

A: One side is not true i have given the contradiction.

Q: Let f(x) = |x|/x . Prove that limx→x0 f(x) does not exist by using a sequential argument.

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Q: (x+1 Q. #7 For the function g(x) = 3 if x 2 constant "b" that makes g(x) continuous at x=2 Final…

A: g(x) is continuous    here we find value of b by using condition of continuous function

Q: Let 2x - x if 0 4 (a) For each of the numbers 2, 3, and 4, dctcrmine whether g is continuous from…

A: We are given                 . For (a), For each numbers 2, 3, and 4, we need to determine whether g…

Q: 8. Suppose that f is a continuous function with f(x) > 0 for all real numbers x, and lim f(x) = 0 =…

A: Consider the provided question, Suppose that f is a continuous function with f (x)>0 for all real…

Q: 1). Does the left-side limit of the difference quotient of the function g(w)=|w| exist at w=0? If it…

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Q: 4. Let function g: R → R be defined by g(x) = |x|. g(0+h)-g(0) h B. The value of lim 9(0+ h) − g(0)…

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Q: 3. Sketch the graph of a function f such that the following conditions are true: ● f(4) is not…

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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.