10. If functions fix) and gx) are continuous everywhere, then A. (f/g) (x) is also continuous everywhere B. (f/g(x) is also continuous everywhere except at the zeroes of g(x) C. more information is needed to answer this question D. the question is insufficient

Q: Show that f(x) = x² + 12x +41 -2 -x² 12x - 31 ifa >-6 2 if x < -6 if x = -6 has a removable…

A: The given function,The aim is to prove the function has a removable discontinuous at  and redefine…

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Q: Justify that 12-21-3 if x + 3, f(x) = 4 I-3 if x = 3

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Q: o Function f₁: R → R is defined by f₁ (x) = (x + 1)². • Function f2: R → R is defined by f2(x) =…

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Q: 3) Consider the function defined piece-wise as follows: f(x) = 4x + 1 for x < 0 and f(x) = (4x - 1)2…

A: The function piecewise defined as follows: fx=4x+1for x&lt;0(4x-1)2for x≥0

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Q: Suppose that a function f is analytic on the interval (1, 10). Suppose that another function g is…

A: Given  Suppose that a function f is analytic on the interval (1, 10). Suppose that another function…

Q: Each of the following functions is defined at x = 3 but not differentiable at x = 3. Cleary explain…

A: Topic :- Differentiability

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Q: Let f(x) = logox and g(x)=₁*. For all x g(x).

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Q: 3. Determine algebraically whether the following functions are odd, even, or neither. x? a) f(x)= x?…

A: 3(a) Given function is fx=x2x2+4. Definition:- Let fx be a function then If f−x=fx then function is…

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.