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3 years ago

Find the limit and confirm using the Sandwich Theorem: lim x->infinity (1 - cosx) / (x^2)

1 answer:

6 0

We are given with the expression <span> (1 - cos x) / (x^2)</span><span> and asked to evaluate the expression to limit as theta approaches zero. In this case, we substitute first zero. cos infinity is 1. The answer is zero over zero. This is indeterminate so we derive the terms according to L'hopital's rule. The derivative is sin x /2x. sin infinity is 1. 1/infinity is equal to zero. Hence the answer is zero.</span>

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Hey there!

Multiply 50 and 4 and you would get 200

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$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

let us first start with some basic information ~

A fraction can be represented as $\frac{x}{y}\\$ where ,

x is the numerator and y is the denominator !

the question asks us to do something that will help us get same denominator for both the terms !

so let's see what we should do in such a case ~

$\frac{9}{10} \: and \: \frac{7}{8} \\ \\ \\ lets \: make \: the \: denominator \: of \: both \\ the \: terms \: reach \: 80 \: , \\ \\ \bold\orange{ \implies \: \frac{9}{10} \times \frac{8}{8} = }\bold\red{ \frac{72}{80}} \\ \\\bold\orange{ \implies \: \frac{7}{8} \times \frac{10}{10} =}\bold\red{ \frac{70}{80}}$

and we're done !

let's add some more info to be lil more clear ~

while converting the denominator of both the terms , we must multiply the same number ( this number refers to the one we'll have to multiply to the denominator to obtain the desired result ) with the denominator as well as with the numerator !

hope helpful :D

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