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AllQuestion and Answers: Page 125

Question Number 204373 Answers: 1 Comments: 0

3^x −2^x =65 x=?

Question Number 204372 Answers: 2 Comments: 0

If , f : [ 0 , b] →^(continuous) R , g : R →_(b−periodic) ^(continuous) R ⇒ lim_(n→∞) ∫_0 ^( b) f(x)g(nx)dx=^? (1/b) ∫_0 ^( b) f(x)dx .∫_0 ^( b) g(x)dx

$I f, f : [0, b] \overset{c o n t i n u o u s}{\to} R$ $, g : R \underset{b - p e r i o d i c}{\overset{c o n t i n u o u s}{\to}} R$ $\Rightarrow {l i m}_{n \to \infty} \int_{0}^{b} f (x) g (n x) d x \overset{?}{=} \frac{1}{b} \int_{0}^{b} f (x) d x . \int_{0}^{b} g (x) d x$

Question Number 204384 Answers: 0 Comments: 1

Question Number 204360 Answers: 3 Comments: 0

if lim_(x→+∞) [(((a+6)x+1)/(ax+1))]=2→ find the largest and smallest correct value for a.

$i f$ $\lim_{x \to + \infty} [\frac{(a + 6) x + 1}{a x + 1}] = 2 \to$ $f i n d t h e l a r g e s t a n d s m a l l e s t c o r r e c t$ $v a l u e f o r a .$

Question Number 204350 Answers: 1 Comments: 0

Question Number 204349 Answers: 1 Comments: 2

Question Number 204348 Answers: 1 Comments: 0

3×7×11 + 7×11×15 + 11×15×19 + ..........+ 39×43×47 = ?

$3 \times 7 \times 11 + 7 \times 11 \times 15 + 11 \times 15 \times 19 + . . . . . . . . . . + 39 \times 43 \times 47 = ?$

Question Number 204346 Answers: 0 Comments: 0

Question Number 204344 Answers: 1 Comments: 2

ctg^6 ((π/9))−9∙ctg^4 ((π/9))+11∙ctg^2 ((π/9))=?

${ctg}^{6} (\frac{π}{9}) - 9 \cdot {ctg}^{4} (\frac{π}{9}) + 11 \cdot {ctg}^{2} (\frac{π}{9}) = ?$

Question Number 204337 Answers: 1 Comments: 0

Question Number 204334 Answers: 2 Comments: 0

Question Number 204330 Answers: 1 Comments: 0

Question Number 204329 Answers: 2 Comments: 0

solve (1/([x]))+(1/([2x]))={x}+(1/3)

$s o l v e \frac{1}{[x]} + \frac{1}{[2 x]} = {x} + \frac{1}{3}$

Question Number 204328 Answers: 0 Comments: 1

Question Number 204323 Answers: 0 Comments: 0

Question Number 204321 Answers: 0 Comments: 0

Question Number 204318 Answers: 1 Comments: 0

Question Number 204313 Answers: 1 Comments: 0

lim((3×^2 −8×−16)/(2×^2 9×+4))

$l i m \frac{3 \times^{2} - 8 \times - 16}{2 \times^{2} 9 \times + 4}$

Question Number 204303 Answers: 1 Comments: 0

Question Number 204302 Answers: 1 Comments: 0

Question Number 204300 Answers: 1 Comments: 0

x^2 log_3 x^2 −(2x^2 +3)log_9 (2x+3)=3log_3 ((x/(2x+3)))

$x^{2} \log_{3} x^{2} - (2 x^{2} + 3) \log_{9} (2 x + 3) = {3 \log}_{3} (\frac{x}{2 x + 3})$

Question Number 204293 Answers: 1 Comments: 1

Prove the following trig identity: ((2sinα+sin3α+sin5α)/(cosα−2cos2α+cos3α))=((2cos2α)/(tan(α/2)))

$Prove the following trig identity :$ $\frac{2 \sin α + \sin 3 α + \sin 5 α}{\cos α - 2 \cos 2 α + \cos 3 α} = \frac{2 \cos 2 α}{\tan \frac{α}{2}}$

Question Number 204279 Answers: 0 Comments: 1

Question Number 204278 Answers: 1 Comments: 3

cos x+cos 3x+cos 5x=(√2)+1 sin x+sin3x+ sin 5x=1 tan 3x=?

$\cos x + \cos 3 x + \cos 5 x = \sqrt{2} + 1$ $\sin x + \sin 3 x + \sin 5 x = 1$ $\tan 3 x = ?$

Question Number 204276 Answers: 0 Comments: 0

Question Number 204275 Answers: 1 Comments: 0

Show that ∫_0 ^(π/4) (√(tan x)) (√(1−tan x)) dx=(((√((√2)−1))/( (√2)))−1)π

$Show that$ $\underset{0}{\int^{\frac{π}{4}}} \sqrt{\tan x} \sqrt{1 - \tan x} d x = (\frac{\sqrt{\sqrt{2} - 1}}{\sqrt{2}} - 1) π$

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