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1. a. What is indeterminate form? Find the limit of the following functions cos x In (x – a) lim x-a* In (ex – eª) lim (1+ sin 4x)cotx

1. a. What is indeterminate form? Find the limit of the following functions cos x In (x – a) lim x-a* In (ex – eª) lim (1+ sin 4x)cotx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. a. What is indeterminate form? Find the limit of the following functions cos x In (x – a) lim x-a* In (ex – eª) lim (1+ sin 4x)cotx b. If f(x) = 2cose + cos² 0,0 < 0 < 27, find where f is increasing, decreasing, intervals of concavity and inflection points.
Transcribed Image Text:1. a. What is indeterminate form? Find the limit of the following functions cos x In (x – a) lim x-a* In (ex – eª) lim (1+ sin 4x)cotx b. If f(x) = 2cose + cos² 0,0 < 0 < 27, find where f is increasing, decreasing, intervals of concavity and inflection points.
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Indeterminate form:

When we need to evaluate the limit of a function at a certain point but after putting the limits the function is of the form:

00, ∞∞, 0×∞, ∞-∞, 00, 1∞, ∞0

If we get a limit of such a form then it is not possible to determine the limit. 

 

We use L-hospital's rule to determine the limit in such a case.

If limx→afxgx=indeterminate

Then to evaluate this we use limx→afxgx=limx→adfxdxdgxdx

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