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AllQuestion and Answers: Page 109

Question Number 205371 Answers: 1 Comments: 2

Question Number 205367 Answers: 1 Comments: 0

Question Number 205353 Answers: 2 Comments: 0

If ax^2 + bx + c = 0 had two roots p and q and p^2 + q^2 = p^3 + q^3 then show that b^3 − 2a^2 c + ab^2 = 3abc.

$If {a x}^{2} + b x + c = 0 had two roots p and q$ $and p^{2} + q^{2} = p^{3} + q^{3} then show that$ $b^{3} - 2 a^{2} c + {a b}^{2} = 3 a b c .$

Question Number 205350 Answers: 1 Comments: 2

A man invested U24000.00 in U5.00 shares of a firm. After a period of time, it appreciated to U5.50 per share. How much dividend did he receive, if the dividend declared is 50k per share?

$A m a n i n v e s t e d U 24000.00 i n U 5.00$ $s h a r e s o f a f i r m . A f t e r a p e r i o d o f$ $t i m e, i t a p p r e c i a t e d t o U 5.50 p e r s h a r e .$ $H o w m u c h d i v i d e n d d i d h e r e c e i v e, i f$ $t h e d i v i d e n d d e c l a r e d i s 50 k p e r s h a r e ?$

Question Number 205360 Answers: 2 Comments: 0

Question Number 205338 Answers: 2 Comments: 0

Question Number 205339 Answers: 1 Comments: 0

lim_(x→0) ((tan(tanx))/(sin(1−cosx)))

$\lim_{x \to 0} \frac{\tan (\tan x)}{\sin (1 - \cos x)}$

Question Number 205335 Answers: 0 Comments: 0

∫((ax+b)/((x^2 −cx+d)^n ))dx

$\int \frac{a x + b}{{(x^{2} - c x + d)}^{n}} d x$

Question Number 205334 Answers: 1 Comments: 1

Question Number 205332 Answers: 0 Comments: 0

determin a) U_(nεN^∗ ) (1,(1/n))

$d e t e r m i n$ $a) \underset{n ϵ N^{*}}{U} (1, \frac{1}{n})$

Question Number 205324 Answers: 3 Comments: 0

Compare: 37^(37) and 36^(38)

$Compare :$ $37^{37} and 36^{38}$

Question Number 205323 Answers: 0 Comments: 1

If log_(√((a^2 +b^2 )/2)) ((a+b)/b)≥log_(√(ab)) (2/((1/a)+(1/b))) when a>1 b>1

$I f {l o g}_{\sqrt{\frac{a^{2} + b^{2}}{2}}} \frac{a + b}{b} ⩾ {l o g}_{\sqrt{a b}} \frac{2}{\frac{1}{a} + \frac{1}{b}}$ $w h e n a > 1 b > 1$

Question Number 205321 Answers: 1 Comments: 0

a^→ =i^ +3j^ +4k^ b^→ =2i^ −3j^ +4k^ c^→ =5i^ −2j^ +4k^ given that p^→ ×b^→ =b^→ ×c^→ and p^→ .b^→ =0 then the value of p^→ (i^ −j^ +k^ )is

$\vec{a} = \hat{i} + 3 \hat{j} + 4 \hat{k} \vec{b} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k} \vec{c} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k} g i v e n t h a t \vec{p} \times \vec{b} = \vec{b} \times \vec{c} a n d \vec{p} . \vec{b} = 0 t h e n t h e v a l u e o f \vec{p} (\hat{i} - \hat{j} + \hat{k}) i s$

Question Number 205319 Answers: 0 Comments: 0

Question Number 205318 Answers: 0 Comments: 0

]^(]^ ]∡)

$Missing \left or extra \right$

Question Number 205315 Answers: 1 Comments: 0

Question Number 205307 Answers: 1 Comments: 1

lim_(n→∞) ((⌊a⌋+⌊2a⌋+...+⌊na⌋)/n^2 ) where a∈R and ⌊x⌋ is the floor of x ∈ R

$\lim_{n \to \infty} \frac{⌊ a ⌋ + ⌊ 2 a ⌋ + . . . + ⌊ n a ⌋}{n^{2}} where a \in R$ $and ⌊ x ⌋ is the floor of x \in R$

Question Number 205306 Answers: 1 Comments: 0

Question Number 205302 Answers: 1 Comments: 0

Question Number 205294 Answers: 1 Comments: 0

∫((3x−x^3 ))^(1/3) dx

$\int \sqrt[3]{3 x - x^{3}} d x$

Question Number 205289 Answers: 0 Comments: 0

Question Number 205288 Answers: 0 Comments: 0

Question Number 205284 Answers: 0 Comments: 0

Question Number 205297 Answers: 2 Comments: 0

Find the′′ range ′′ of : i : f (x) =⌊ (( x)/( ⌊ x ⌋)) ⌋ ii: f(x) = (( x)/(⌊ x ⌋ + ⌊ −x ⌋))

$F i n d {t h e}^{″} r a n g e^{″} o f :$ $i : f (x) = ⌊ \frac{x}{⌊ x ⌋} ⌋$ $i i : f (x) = \frac{x}{⌊ x ⌋ + ⌊ - x ⌋}$

Question Number 205280 Answers: 0 Comments: 1

Question Number 205279 Answers: 1 Comments: 0

∫^(π/2) _(-π/2) ((8(√2)cosx)/((1+e^(sinx) )(1+sin^4 x)))dx=aπ+blog(3+2(√2)) then find a+b

${\int_{- π / 2}}^{π / 2} \frac{8 \sqrt{2} c o s x}{(1 + \overset{s i n x}{e}) (1 + s i \overset{4}{n x})} d x = a π + b l o g (3 + 2 \sqrt{2}) t h e n f i n d a + b$

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