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LimitsQuestion and Answers: Page 10

Question Number 193976 Answers: 2 Comments: 0

Question Number 193874 Answers: 1 Comments: 0

Question Number 193863 Answers: 2 Comments: 0

lim_(x→0) ((1−(1/2)x^2 −cos ((x/(1−x^2 ))))/x^4 ) =?

$\lim_{x \to 0} \frac{1 - \frac{1}{2} x^{2} - \cos (\frac{x}{1 - x^{2}})}{x^{4}} = ?$

Question Number 193819 Answers: 1 Comments: 0

lim_(x→0) cos ((((Π/3)+x)/x))

$\underset{x \to 0}{\lim c o s} (\frac{\frac{Π}{3} + x}{x})$

Question Number 193803 Answers: 1 Comments: 0

lim_(x→2) (((√(11−x)) cos ((π/(x−2))))/(cot (x−2)))=?

$\lim_{x \to 2} \frac{\sqrt{11 - x} \cos (\frac{π}{x - 2})}{\cot (x - 2)} = ?$

Question Number 193596 Answers: 2 Comments: 0

Question Number 193563 Answers: 3 Comments: 0

Question Number 193540 Answers: 0 Comments: 0

Question Number 193532 Answers: 2 Comments: 0

lim_(x→2) ((1−cos πx)/((2−x)^2 )) =?

$\lim_{x \to 2} \frac{1 - \cos π x}{{(2 - x)}^{2}} = ?$

Question Number 193408 Answers: 1 Comments: 0

$\underset{―}{\underset{⏟}{}}$

Question Number 193328 Answers: 1 Comments: 0

f(x)= { ((((x^2 −x)/(x^2 −1)) ; x≠1)),((2x+1; x=1)) :} thene find lim_(x→1) f(x)=?

$f (x) = {\begin{cases} \frac{x^{2} - x}{x^{2} - 1}; x \neq 1 \\ 2 x + 1; x = 1 \end{cases}$ $thene find \lim_{x \to 1} f (x) = ?$

Question Number 193248 Answers: 1 Comments: 0

L= lim_( x→0) (( sin(x )−arcsin(x))/(tan(x)− arctan(x)))=?

$L = \lim_{x \to 0} \frac{\sin (x) - \arcsin (x)}{\tan (x) - \arctan (x)} = ?$

Question Number 193236 Answers: 2 Comments: 0

Question Number 193117 Answers: 3 Comments: 0

lim_(x→0) (cosx)^(1/x)

$\lim_{x \to 0} {(cosx)}^{\frac{1}{x}}$

Question Number 192969 Answers: 2 Comments: 1

Question Number 192867 Answers: 1 Comments: 0

derivate of csc(2x) by definition

$d e r i v a t e o f c s c (2 x) b y d e f i n i t i o n$

Question Number 192846 Answers: 1 Comments: 0

lim_(h→0) ((3h)/( ((3h+x))^(1/5) −(x)^(1/5) ))=?

$\lim_{h \to 0} \frac{3 h}{\sqrt[5]{3 h + x} - \sqrt[5]{x}} = ?$

Question Number 192841 Answers: 1 Comments: 0

Question Number 192652 Answers: 2 Comments: 0

lim_(x→0) ((1−(√(cos(x))))/(1+cos((√x))))

${l i m}_{x \to 0} \frac{1 - \sqrt{c o s (x)}}{1 + c o s (\sqrt{x})}$

Question Number 192651 Answers: 2 Comments: 0

lim_(x→0) ((2−(√(cos(x)))−cos(x))/x^2 )

${l i m}_{x \to 0} \frac{2 - \sqrt{c o s (x)} - c o s (x)}{x^{2}}$

Question Number 192650 Answers: 2 Comments: 0

lim_(x→0) ((x−sen(x))/(tan^3 (x))) without lhopital rule

$\lim_{x \to 0} \frac{x - s e n (x)}{{t a n}^{3} (x)}$ $w i t h o u t l h o p i t a l r u l e$

Question Number 192646 Answers: 1 Comments: 0

lim_(x⇒3) (√((x^2 −4x+3)/(x−3))) find the limit

$\lim_{x \Rightarrow 3} \sqrt{\frac{x^{2} - 4 x + 3}{x - 3}}$ $find the limit$

Question Number 192639 Answers: 2 Comments: 0

lim_(x⇒∝ ) ((3x^3 +3x^2 +1)/(5x^3 +4x^2 +x)) find the limit

Question Number 192617 Answers: 2 Comments: 0

Question Number 192616 Answers: 0 Comments: 0

Question Number 192573 Answers: 0 Comments: 0

solve; lim_(x→0) x^2 tan(((sinπx)/(2x))) solution let L=lim_(x→0) x^2 tan(((sinπx)/(2x))) since sinx∼x−(x^3 /6) L=lim_(x→0) x^2 tan(((πx)/(2x))−((π^3 x^3 )/(12x))) L=lim_(x→0) x^2 tan((π/2)−((π^3 x^2 )/(12))) since tan((π/2)−x)=(1/(tanx)) L=lim_(x→0) (x^2 /(tan(((π^3 x^2 )/(12))))) L=lim_(x→0) (((π^3 x^2 )/(12))/(tan(((π^3 x^2 )/(12))))) ((12)/π^3 ) L=((12)/π^3 )lim_(x→0) (((π^3 x^2 )/(12))/(tan(((π^3 x^2 )/(12))))) since lim_(x→0) (x/(tanx))=1 L=((12)/π^3 ) ∙1=((12)/π^3 ) solved by HY a.k.a senestro

$s o l v e;$ $\lim_{x \to 0} x^{2} t a n (\frac{s i n π x}{2 x})$ $s o l u t i o n$ $l e t L = \lim_{x \to 0} x^{2} t a n (\frac{s i n π x}{2 x})$ $s i n c e s i n x \sim x - \frac{x^{3}}{6}$ $L = \lim_{x \to 0} x^{2} t a n (\frac{π x}{2 x} - \frac{π^{3} x^{3}}{12 x})$ $L = \lim_{x \to 0} x^{2} t a n (\frac{π}{2} - \frac{π^{3} x^{2}}{12})$ $s i n c e t a n (\frac{π}{2} - x) = \frac{1}{t a n x}$ $L = \lim_{x \to 0} \frac{x^{2}}{t a n (\frac{π^{3} x^{2}}{12})}$ $L = \lim_{x \to 0} \frac{\frac{π^{3} x^{2}}{12}}{t a n (\frac{π^{3} x^{2}}{12})} \frac{12}{π^{3}}$ $L = \frac{12}{π^{3}} \lim_{x \to 0} \frac{\frac{π^{3} x^{2}}{12}}{t a n (\frac{π^{3} x^{2}}{12})}$ $s i n c e \lim_{x \to 0} \frac{x}{t a n x} = 1$ $L = \frac{12}{π^{3}} \cdot 1 = \frac{12}{π^{3}}$ $s o l v e d b y H Y a . k . a s e n e s t r o$

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