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Question Number 142140 Answers: 1 Comments: 0

[lim_(x→0) ((sin x)/x)]=? lim_(x→0) {[((100sin^(−1) x)/x)]+[((100tan^(−1) x)/x)]}=? lim_(x→0) {[((100x)/(sin^(−1) x))]+[((100x)/(tan^(−1) x))]}=? where [x] denotes greatest integer less than or equal to x. solution please

$$\left[\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{{x}}\right]=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100sin}^{−\mathrm{1}} {x}}{{x}}\right]+\left[\frac{\mathrm{100tan}^{−\mathrm{1}} {x}}{{x}}\right]\right\}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100}{x}}{\mathrm{sin}^{−\mathrm{1}} {x}}\right]+\left[\frac{\mathrm{100}{x}}{\mathrm{tan}^{−\mathrm{1}} {x}}\right]\right\}=? \\ $$$${where}\:\left[{x}\right]\:{denotes}\:{greatest}\:{integer}\: \\ $$$${less}\:{than}\:{or}\:{equal}\:{to}\:{x}. \\ $$$${solution}\:{please} \\ $$

Question Number 142138 Answers: 0 Comments: 6

(√(y^2 +1)) + (√(x^2 +4)) + (√(z^2 +9)) = 10 x+y+z=?

$$\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}\:+\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:+\:\sqrt{{z}^{\mathrm{2}} +\mathrm{9}}\:=\:\mathrm{10} \\ $$$${x}+{y}+{z}=? \\ $$

Question Number 142131 Answers: 1 Comments: 1

∫(dx/(3+2sinx+cosx))dx

$$\int\frac{{dx}}{\mathrm{3}+\mathrm{2}{sinx}+{cosx}}{dx} \\ $$

Question Number 142120 Answers: 2 Comments: 2

Question Number 142116 Answers: 2 Comments: 0

use trigonometric substitution to solve ∫(x^3 /( (√(9−x^2 ))))dx

$${use}\:{trigonometric}\:{substitution}\:{to}\:{solve} \\ $$$$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 142115 Answers: 2 Comments: 0

simplify A_n (x)=(1+ix)^n +(1−ix)^n x from C

$$\mathrm{simplify}\:\:\mathrm{A}_{\mathrm{n}} \left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}\right)^{\mathrm{n}} +\left(\mathrm{1}−\mathrm{ix}\right)^{\mathrm{n}} \:\:\:\mathrm{x}\:\mathrm{from}\:\mathrm{C} \\ $$

Question Number 142105 Answers: 2 Comments: 0

Sum the series to n terms sin θ−sin 2θ+sin 3θ−........

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms} \\ $$$$\mathrm{sin}\:\theta−\mathrm{sin}\:\mathrm{2}\theta+\mathrm{sin}\:\mathrm{3}\theta−........ \\ $$

Question Number 142269 Answers: 0 Comments: 0

Question Number 142268 Answers: 0 Comments: 0

∫(e^x /(cosx))dx

$$\int\frac{{e}^{{x}} }{{cosx}}{dx} \\ $$

Question Number 142100 Answers: 2 Comments: 0

∫^ (1/(1+(√(1+t)) )) dt=?

$$\:\:\:\:\:\:\int^{\:} \:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{1}+{t}}\:}\:{dt}=? \\ $$

Question Number 142096 Answers: 0 Comments: 1

Question Number 142092 Answers: 0 Comments: 1

Question Number 142085 Answers: 2 Comments: 0

Proof that 1+3n<n^2 for every positive integer n≥4

$${Proof}\:{that}\:\mathrm{1}+\mathrm{3}{n}<{n}^{\mathrm{2}} \:{for}\:{every}\:{positive}\:{integer}\:{n}\geqslant\mathrm{4} \\ $$

Question Number 142079 Answers: 3 Comments: 0

y=(dy/dx)+(d^2 y/dx^2 )+(d^3 y/dx^3 )+..... solve this diffrential equation

$${y}=\frac{{dy}}{{dx}}+\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }+..... \\ $$$${solve}\:{this}\:{diffrential}\:{equation} \\ $$

Question Number 142061 Answers: 0 Comments: 3

(√(5x^2 +y^2 +z^2 +2x+2+2xy−4xz+10)) + ∣2x−y−13∣ = 3

$$\sqrt{\mathrm{5}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}+\mathrm{2}{xy}−\mathrm{4}{xz}+\mathrm{10}}\:+ \\ $$$$\mid\mathrm{2}{x}−{y}−\mathrm{13}\mid\:=\:\mathrm{3}\: \\ $$

Question Number 142060 Answers: 2 Comments: 0

Question Number 142045 Answers: 2 Comments: 0

Question Number 142041 Answers: 3 Comments: 0

Question Number 142052 Answers: 3 Comments: 0

Given that fog(x)=((2x−1)/x) and g(x)=5x+2, Find f(x).

$$\boldsymbol{\mathrm{Given}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{fog}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{1}}{\boldsymbol{\mathrm{x}}}\:\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{5}\boldsymbol{\mathrm{x}}+\mathrm{2}, \\ $$$$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right). \\ $$$$ \\ $$

Question Number 142049 Answers: 2 Comments: 0

∫_1 ^( 3) e^x^2 dx help me sir

$$\int_{\mathrm{1}} ^{\:\mathrm{3}} {e}^{{x}^{\mathrm{2}} } {dx} \\ $$$${help}\:{me}\:{sir}\: \\ $$

Question Number 142035 Answers: 1 Comments: 0

(1/2^(1/4) ).(3^(1/9) /4^(1/16) ).(5^(1/25) /6^(1/36) ).(7^(1/49) /8^(1/64) )...=exp(−((ζ′(2))/2)−(π^2 /(12))log (2))

$$\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}/\mathrm{4}} }.\frac{\mathrm{3}^{\mathrm{1}/\mathrm{9}} }{\mathrm{4}^{\mathrm{1}/\mathrm{16}} }.\frac{\mathrm{5}^{\mathrm{1}/\mathrm{25}} }{\mathrm{6}^{\mathrm{1}/\mathrm{36}} }.\frac{\mathrm{7}^{\mathrm{1}/\mathrm{49}} }{\mathrm{8}^{\mathrm{1}/\mathrm{64}} }...={exp}\left(−\frac{\zeta'\left(\mathrm{2}\right)}{\mathrm{2}}−\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\mathrm{log}\:\left(\mathrm{2}\right)\right) \\ $$

Question Number 142036 Answers: 0 Comments: 0

Question Number 142028 Answers: 2 Comments: 0

............Calculus......... ∫_0 ^( ∞) ((sin(sin(x)).e^(cos(x)) )/x)dx=??? ............m.n.....

$$\:\:\:\:\:\:\:\:............{Calculus}.........\: \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({sin}\left({x}\right)\right).{e}^{{cos}\left({x}\right)} }{{x}}{dx}=??? \\ $$$$\:............{m}.{n}..... \\ $$

Question Number 142023 Answers: 1 Comments: 0

S_n =Σ_(k=0) ^n (1/((n−k)!(n+k)!)) =??

$$\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{n}−\mathrm{k}\right)!\left(\mathrm{n}+\mathrm{k}\right)!}\:=?? \\ $$

Question Number 142022 Answers: 1 Comments: 0

Question Number 142021 Answers: 0 Comments: 0

simplfy f(x)=tan(α arcsinx) and g(x)=tan(α arcosx) α is real x∈[−1,1]

$$\mathrm{simplfy}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{tan}\left(\alpha\:\mathrm{arcsinx}\right) \\ $$$$\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{tan}\left(\alpha\:\mathrm{arcosx}\right)\:\:\alpha\:\mathrm{is}\:\mathrm{real} \\ $$$$\mathrm{x}\in\left[−\mathrm{1},\mathrm{1}\right] \\ $$

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