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LimitsQuestion and Answers: Page 9

Question Number 195033 Answers: 1 Comments: 0

any point is the function is not continous f(x)=(4x+8)^((ln45)/8) a) −8 b) −2 c) no one d) 5

$a n y p o i n t i s t h e f u n c t i o n i s$ $n o t c o n t i n o u s$ $f (x) = {(4 x + 8)}^{\frac{l n 45}{8}}$ $a) - 8 b) - 2$ $c) n o o n e d) 5$

Question Number 195029 Answers: 1 Comments: 0

$\underset{⏟}{}$

Question Number 195021 Answers: 1 Comments: 0

lim_(x→0) ((x−sin x)/x^n )=¿ (n∈N^∗ )

$\lim_{x \to 0} \frac{x - s i n x}{x^{n}} = ¿ (n \in N^{*})$

Question Number 195013 Answers: 1 Comments: 0

lim_(x→3) (((2((√6)−(√(2x)) +(√(6−2x))))/( (√(36−4x^2 )))) )

$\lim_{x \to 3} (\frac{2 (\sqrt{6} - \sqrt{2 x} + \sqrt{6 - 2 x})}{\sqrt{36 - {4 x}^{2}}})$

Question Number 194968 Answers: 2 Comments: 0

Question Number 194928 Answers: 1 Comments: 0

lim_(x→∞) ((√(x^2 +5x+1)) +(√(x^2 −2x+1))+(√(x^2 +3))+(√(x^2 −4x+9))−(√(16x^2 −8)) =?

$\lim_{x \to \infty} (\sqrt{x^{2} + 5 x + 1} + \sqrt{x^{2} - 2 x + 1} + \sqrt{x^{2} + 3} + \sqrt{x^{2} - 4 x + 9} - \sqrt{16 x^{2} - 8} = ?$

Question Number 194891 Answers: 1 Comments: 0

lim_(x→3^+ ) ((((√x)−(√(x−3))−(√3))/( (√(x^2 −9)))) )=?

$\lim_{x \to 3^{+}} (\frac{\sqrt{x} - \sqrt{x - 3} - \sqrt{3}}{\sqrt{x^{2} - 9}}) = ?$

Question Number 194879 Answers: 1 Comments: 0

Question Number 194685 Answers: 1 Comments: 0

Question Number 194640 Answers: 1 Comments: 0

$\underset{⏟}{}$

Question Number 194482 Answers: 1 Comments: 0

determinant ((( ⋐)))

$\begin{matrix} \underset{―}{\underset{⏟}{⋐}} \end{matrix}$

Question Number 194466 Answers: 2 Comments: 0

⋐

$⋐$

Question Number 194462 Answers: 1 Comments: 0

Prove that ∫^( +∞^ ) _( 0) ((1−e^(−x^2 ) )/x^2 )dx=(√𝛑)

$Prove that {\int_{0}}^{+ \infty^{}} \frac{1 - e^{- x^{2}}}{x^{2}} d x = \sqrt{π}$

Question Number 194451 Answers: 1 Comments: 0

⊪

$\underset{―}{\underset{⏟}{⊪}}$

Question Number 194425 Answers: 1 Comments: 0

$\underset{⏟}{}$

Question Number 194344 Answers: 2 Comments: 0

Question Number 194338 Answers: 2 Comments: 0

Question Number 194335 Answers: 1 Comments: 0

Question Number 194334 Answers: 0 Comments: 2

^()

$\underset{⏟}{^{}}$

Question Number 194282 Answers: 1 Comments: 0

f(f(x)) = ax + b 1. show that f(ax+b) = af(x) + b deduce f ′(ax + b) 2. Show that f ′(x) is a constant hence deduce f

$f (f (x)) = a x + b$ $1 . s h o w t h a t f (a x + b) = a f (x) + b$ $d e d u c e f^{'} (a x + b)$ $2 . S h o w t h a t f^{'} (x) i s a c o n s t a n t$ $h e n c e d e d u c e f$

Question Number 194279 Answers: 1 Comments: 0

$\underset{⏟}{}$

Question Number 194256 Answers: 2 Comments: 0

lim_(x→0) ((((1+tan x)/(1−tan x)) −1)/x) =?

$\lim_{x \to 0} \frac{\frac{1 + \tan x}{1 - \tan x} - 1}{x} = ?$

Question Number 194250 Answers: 2 Comments: 0

find the value of a for which the limit lim_(x→0) ((sin (ax)−tan^(−1) (x)−x)/(x^3 +x^4 )) is finite and then evaluate the limit

$find the value of a for which the limit$ $\lim_{x \to 0} \frac{\sin (ax) - \tan^{- 1} (x) - x}{x^{3} + x^{4}} is finite$ $and then evaluate the limit$

Question Number 194185 Answers: 1 Comments: 0

lim_( x→ 0^( −) ) { (( x^( 2) +2cos(x) + ⌊−((tan(x))/x) ⌋)/(ax^( 4) )) } = 1 a = ? a: (1/(12)) b: −(1/2) c: 12 d: −12

$\lim_{x \to 0^{-}} {\frac{x^{2} + 2 c o s (x) + ⌊ - \frac{t a n (x)}{x} ⌋}{{a x}^{4}}} = 1$ $a = ?$ $a : \frac{1}{12} b : - \frac{1}{2} c : 12 d : - 12$

Question Number 194139 Answers: 1 Comments: 1

Question Number 194020 Answers: 0 Comments: 0

F_n = F_n _(−1) +F_(n−2) F_2 = F_1 =1 F_n : 1 , 1 , 2 , 3 ,5... f(x)= Σ_(n=1) ^∞ F_n x^( n) = x + x^( 2) +Σ_(n=3) ^∞ (F_(n−1) +F_(n−2) )x^( n) = x+x^2 + Σ_(n=3) ^∞ F_(n−1) x^( n) + x^( 2) f (x) = x + x^( 2) + x^( 2) f(x) +x Σ_(n=2) ^∞ F_n x^( n) = x + x^( 2) + x^( 2) f(x)−x^( 2) + xf(x) ∴ f(x)= (x/(1−x−x^( 2) )) (generating function ) (x/(1−x−x^( 2) )) =Σ_(n=1) ^∞ F_n x^( n) ⇒ (x^( 2) /(1−x−x^( 2) ))=Σ_(n=1) ^∞ F_n x^( n+1) x= (1/(10)) ⇒ ((1/(100))/(1−(1/(10))−(1/(100)))) = Σ_(n=1) ^∞ (F_n /(10^( n+1) )) ⇒ { Σ_(n=1) ^∞ (( F_n )/(10^( n+1) )) = (1/(89)) }

$F_{n} = F_{n}_{- 1} + F_{n - 2} F_{2} = F_{1} = 1$ $F_{n} : 1, 1, 2, 3, 5 . . .$ $f (x) = \underset{n = 1}{\sum^{\infty}} F_{n} x^{n} = x + x^{2} + \underset{n = 3}{\sum^{\infty}} (F_{n - 1} + F_{n - 2}) x^{n}$ $= x + x^{2} + \underset{n = 3}{\sum^{\infty}} F_{n - 1} x^{n} + x^{2} f (x)$ $= x + x^{2} + x^{2} f (x) + x \underset{n = 2}{\sum^{\infty}} F_{n} x^{n}$ $= x + x^{2} + x^{2} f (x) - x^{2} + x f (x)$ $∴ f (x) = \frac{x}{1 - x - x^{2}} (g e n e r a t i n g f u n c t i o n)$ $\frac{x}{1 - x - x^{2}} = \underset{n = 1}{\sum^{\infty}} F_{n} x^{n} \Rightarrow \frac{x^{2}}{1 - x - x^{2}} = \underset{n = 1}{\sum^{\infty}} F_{n} x^{n + 1}$ $x = \frac{1}{10} \Rightarrow \frac{\frac{1}{100}}{1 - \frac{1}{10} - \frac{1}{100}} = \underset{n = 1}{\sum^{\infty}} \frac{F_{n}}{10^{n + 1}}$ $\Rightarrow {\underset{n = 1}{\sum^{\infty}} \frac{F_{n}}{10^{n + 1}} = \frac{1}{89}}$

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