Lim x- 2 cos- x - sin- x -1 x-2 - 0- 2

lim_x → 2( cosα)^x + ( sinα)^a 1x 2 ( 0÷0 form) using lim_x → 2ddx( cosα)^x + ddx( sinα)α1 lim_x → 2( cosα)^xlog cosα #160; + ( sinα)^x ...

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Perpendicular Distance of a Point from a Line

lim x→ 2 cos...

Question

$lim x \to 2 (\frac{{(cos α)}^{x} + {(sin α)}^{x} - 1}{x - 2}), α \in (0, \frac{π}{2})$

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(sin α) x + 2 z = 0, (cos α) x + (sin α) y = 0; (cos α) y + 2 z = a

α

lim x \to 2 \frac{(cos α)^{x} + (sin α)^{x} - 1}{x - 2}

Evaluate the following one sided limits:

$(i) {lim}_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}$

$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

$(i i i) {lim}_{x \to 0^{+}} \frac{1}{3 x}$

$(i v) {lim}_{x \to 8^{+}} \frac{2 x}{x + 8}$

$(v) {lim}_{x \to 0^{+}} \frac{2}{x^{\frac{1}{5}}}$

$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

$(v i i) {lim}_{x \to \frac{π}{2^{+}}} s e c x$

$(v i i i) {lim}_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}$

$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

$(x) {lim}_{x \to 0^{+}} (2 - c o t x)$

$(x i) {lim}_{x \to 0^{-}} 1 + c o s e c x$

lim x \to 0 \frac{\sqrt{1 - cos 2 x}}{x}

| sin x | = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} sin x; & 0 < x < \frac{π}{2} - sin x; & - \frac{π}{2} < x < 0 \end{matrix}

\lim_{x \to 2^{+}} \frac{x - 3}{x^{2} - 4}

\lim_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}

\lim_{x \to 0^{+}} \frac{1}{3 x}

\lim_{x \to - 8^{+}} \frac{2 x}{x + 8}

\lim_{x \to 0^{+}} \frac{2}{x^{1 / 5}}

\lim_{x \to \frac{π}{2}} \tan x

\lim_{x \to - π / 2^{+}} \sec x

\lim_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}

\lim_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}

\lim_{x \to 0^{-}} 2 - \cot x

\lim_{x \to 0^{-}} 1 + cosec x

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