Find the limit of fx-cos xx- 2 as x approaches - 2-

The correct option is A 1 f(x)=cos xx π 2 At x=π 2 The expression takes the form 00 Using L`Hospital Rule, #160; #160;lim _x →π 2 f( ...

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L'Hospital Rule to Remove Indeterminate Form

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Question

Find the limit of $f (x) = \frac{cos x}{x - \frac{π}{2}}$ as $x$ approaches $\frac{π}{2}$ .

1

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f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 2 sin x, & - π \leq x \leq \frac{- π}{2} a cos (x) + b, & \frac{- π}{2} < x < 0 - 2 + cos x, & 0 \leq x \leq \frac{π}{2} c sin x, & \frac{π}{2} < x \leq π \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

[- π, π],

f (x)

α

β

f (x)

f (x) = - 2 sin x,

- π \leq x \leq - \frac{π}{2}

= α sin x + β,

- \frac{π}{2} < x < \frac{π}{2}

= cos x,

\frac{π}{2} \leq x \leq π

[- π, π]

f (x) = x^{3} + x^{2} - 10 x, - 1 \leq x < 0

cos x, 0 \leq x < \frac{π}{2}

1 + sin x, \frac{π}{2} \leq x \leq π .

f (x)

The graph of f(x) is given below. The limit of the function f(x) as x approaches 'a' is

f (x) = 1 + [c o s x] x

0 < x \leq \frac{π}{2}

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