If a function has a horizontal asymptote at y = a, then BOTH lim x → ∞ f ( x ) = a AND lim x → − ∞ f ( x ) = a. if g ( x ) = 5 cos ⁡ x, then lim x → ∞ g ( x ) does not exist. If a function h ( x ) has the domain ( − ∞ , 0 ] and h ( x ) has no horizontal asymptote, then it must be the case that either lim x → − ∞ h ( x ) = − ∞

Q: 1. Consider the function f(x) = x(Va – 1), where a > 0, x > 0. (a) Tell if f is an indeterminate…

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Q: The limit below represents a derivative f' (a). Find f(x) and a. 43+h - 64 lim h-0 h f(x) = a =

A: The limit below represents a derivative f'(a) defined byf'(a) = limh→0 43+h-64h  ....(1)we find f(x)…

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A: We have g(x) = x2+x-2x-1  To find :  limx→1+g(x) limx→1+g(x)  =   lim h→0g(1+h)    =…

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A: Given limit - limx→0 fxgx = 6Putting limit as x = 0,f0g0 = 6         .............(1)Given that,f0 =…

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A: Given:  1) limx→432x-3+5 Plug in the value x=4           =324-3+5             =38-3+5…

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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.