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Question Number 105504 Answers: 9 Comments: 0

(1)lim_(x→0) ((∫_( 0) ^( x^2 ) sec^2 t dt)/(x sin x)) ? (2) ∫_(−π/2) ^(π/2) (√(sec x−cos x)) dx ? (3)In a triangle if tan A=2sin 2C and 3cos A=2sin Bsin C. find C

$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\:\mathrm{0}} ^{\:{x}^{\mathrm{2}} } \mathrm{sec}\:^{\mathrm{2}} {t}\:{dt}}{{x}\:\mathrm{sin}\:{x}}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\sqrt{\mathrm{sec}\:{x}−\mathrm{cos}\:{x}}\:{dx}\:? \\ $$$$\left(\mathrm{3}\right){In}\:{a}\:{triangle}\:{if}\:\mathrm{tan}\:{A}=\mathrm{2sin}\:\mathrm{2}{C} \\ $$$${and}\:\mathrm{3cos}\:{A}=\mathrm{2sin}\:{B}\mathrm{sin}\:{C}.\:{find}\:{C} \\ $$

Question Number 105498 Answers: 1 Comments: 3

lim_(n→∞) (Π_(k=1) ^n ((1/k)))^(2/n)

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\frac{\mathrm{1}}{{k}}\right)\right)^{\frac{\mathrm{2}}{{n}}} \\ $$

Question Number 105493 Answers: 0 Comments: 0

Question Number 105491 Answers: 1 Comments: 0

The tax free allowance for Tammy is K3 300.00 and he pays Income Tax at the rate of 30% on the balance of his salary. Calculate the net pay for Tammy if his montly salary is K5 500.00.

$${The}\:{tax}\:{free}\:{allowance}\:{for} \\ $$$${Tammy}\:{is}\:\mathrm{K3}\:\mathrm{300}.\mathrm{00}\:{and}\:{he}\: \\ $$$${pays}\:{Income}\:{Tax}\:{at}\:{the}\:{rate} \\ $$$${of}\:\mathrm{30\%}\:{on}\:{the}\:{balance}\:{of}\:{his}\: \\ $$$${salary}.\:{Calculate}\:{the}\:{net}\:{pay} \\ $$$${for}\:{Tammy}\:{if}\:{his}\:{montly} \\ $$$${salary}\:{is}\:\mathrm{K5}\:\mathrm{500}.\mathrm{00}. \\ $$$$ \\ $$

Question Number 105488 Answers: 1 Comments: 0

if y = cos(x^2 ) then y^((n)) = .........

$${if}\:{y}\:=\:{cos}\left({x}^{\mathrm{2}} \right)\:\:\:\:\:\:{then}\: \\ $$$$\:\:\:\:\:\:{y}^{\left({n}\right)} \:=\:......... \\ $$

Question Number 105487 Answers: 1 Comments: 0

Σ_(k=1) ^∞ k^2 (0.8)^(k−1)

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{k}^{\mathrm{2}} \left(\mathrm{0}.\mathrm{8}\right)^{\mathrm{k}−\mathrm{1}} \\ $$

Question Number 105471 Answers: 0 Comments: 2

Σ_(k=1) ^n ((1/k))^2

$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{{k}}\right)^{\mathrm{2}} \\ $$

Question Number 105476 Answers: 1 Comments: 1

Question Number 105474 Answers: 2 Comments: 0

Question Number 105462 Answers: 0 Comments: 1

App Updates: • Support added for Hindi Language Select Hindi from font menu. • Drawing: Added option to draw an arc at a point connecting two lines (angle and explementary angle) We can add more languages. More languages: If u provide us a 6×10 table(s) with character map for another language (left to right) over email we can add support. Right to left: App still cannot support right to left languages but we are working on enhancing this.

$$\mathrm{App}\:\mathrm{Updates}: \\ $$$$\bullet\:\mathrm{Support}\:\mathrm{added}\:\mathrm{for}\:\mathrm{Hindi}\:\mathrm{Language} \\ $$$$\:\:\:\mathrm{Select}\:\mathrm{Hindi}\:\mathrm{from}\:\mathrm{font}\:\mathrm{menu}. \\ $$$$\bullet\:\mathrm{Drawing}:\:\mathrm{Added}\:\mathrm{option}\:\mathrm{to}\:\mathrm{draw} \\ $$$$\:\:\:\:\mathrm{an}\:\mathrm{arc}\:\mathrm{at}\:\mathrm{a}\:\mathrm{point}\:\mathrm{connecting}\:\mathrm{two} \\ $$$$\:\:\:\:\mathrm{lines}\:\left(\mathrm{angle}\:\mathrm{and}\:\mathrm{explementary}\:\mathrm{angle}\right) \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{add}\:\mathrm{more}\:\mathrm{languages}.\: \\ $$$$\mathrm{More}\:\mathrm{languages}:\:\mathrm{If}\:\mathrm{u}\:\mathrm{provide}\:\mathrm{us} \\ $$$$\mathrm{a}\:\mathrm{6}×\mathrm{10}\:\mathrm{table}\left(\mathrm{s}\right)\:\mathrm{with}\:\mathrm{character}\:\mathrm{map} \\ $$$$\mathrm{for}\:\mathrm{another}\:\mathrm{language}\:\left(\mathrm{left}\:\mathrm{to}\:\mathrm{right}\right) \\ $$$$\mathrm{over}\:\mathrm{email}\:\mathrm{we}\:\mathrm{can}\:\mathrm{add}\:\mathrm{support}.\: \\ $$$$\mathrm{Right}\:\mathrm{to}\:\mathrm{left}:\:\mathrm{App}\:\mathrm{still}\:\mathrm{cannot}\:\mathrm{support} \\ $$$$\mathrm{right}\:\mathrm{to}\:\mathrm{left}\:\mathrm{languages}\:\mathrm{but}\:\mathrm{we}\:\mathrm{are} \\ $$$$\mathrm{working}\:\mathrm{on}\:\mathrm{enhancing}\:\mathrm{this}. \\ $$

Question Number 105643 Answers: 2 Comments: 0

lim_(x→0) ((tan (x−sin x))/(2−(√(4+sin^3 2x))))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left({x}−\mathrm{sin}\:{x}\right)}{\mathrm{2}−\sqrt{\mathrm{4}+\mathrm{sin}\:^{\mathrm{3}} \:\mathrm{2}{x}}} \\ $$

Question Number 105456 Answers: 2 Comments: 0

Prove that the curve y=x^4 +3x^2 +2x does not meet the straight line y=2x−1 and find the distace between their nearest points.(Answer (1/(√5)))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\mathrm{x}^{\mathrm{4}} +\mathrm{3x}^{\mathrm{2}} +\mathrm{2x} \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{meet}\:\mathrm{the}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{y}=\mathrm{2x}−\mathrm{1}\:\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distace}\:\mathrm{between} \\ $$$$\mathrm{their}\:\mathrm{nearest}\:\mathrm{points}.\left(\mathrm{Answer}\:\frac{\mathrm{1}}{\sqrt{\mathrm{5}}}\right) \\ $$

Question Number 105455 Answers: 3 Comments: 0

∫_(−1) ^1 ((e^x −e^(−x) )/(cos x)) dx

$$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{cos}\:{x}}\:{dx}\: \\ $$

Question Number 105448 Answers: 3 Comments: 2

Given { ((((4x^2 )/(4x^2 +1)) = y)),((((4y^2 )/(4y^2 +1)) = z)),((((4z^2 )/(4z^2 +1)) = x)) :} . find x+y+z ?