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Question Number 176005 Answers: 0 Comments: 2

Question Number 175996 Answers: 1 Comments: 0

lim_(x→0) ((a^x −1)/x)=?

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{a}^{{x}} −\mathrm{1}}{{x}}=? \\ $$

Question Number 175995 Answers: 2 Comments: 0

lim_(x→0) ((e^(3x) −1)/x)=?

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{\mathrm{3}{x}} −\mathrm{1}}{{x}}=? \\ $$

Question Number 175994 Answers: 3 Comments: 0

lim_(x→∞) ((e^x −1)/x)=?

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}=? \\ $$

Question Number 175987 Answers: 4 Comments: 0

please calculate I=∫_0 ^(π/2) (dx/(1+(tanx)^(√2) )) J=∫_0 ^π (dx/(a^2 cos^2 x+sin^2 x)) K=∫_0 ^(π/2) (dx/(3tanx+2))

$${please}\:{calculate} \\ $$$${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+\left({tanx}\right)^{\sqrt{\mathrm{2}}} } \\ $$$${J}=\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}} {x}+{sin}^{\mathrm{2}} {x}} \\ $$$${K}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{3}{tanx}+\mathrm{2}} \\ $$

Question Number 175986 Answers: 2 Comments: 0

Question Number 175976 Answers: 1 Comments: 1

Question Number 175972 Answers: 2 Comments: 0

((x^(11) +x)/(x^7 +x^5 )) = ((205)/(16)) solve for x (undecic equation )

$$\frac{{x}^{\mathrm{11}} +{x}}{{x}^{\mathrm{7}} +{x}^{\mathrm{5}} }\:=\:\frac{\mathrm{205}}{\mathrm{16}} \\ $$$${solve}\:{for}\:{x}\:\left({undecic}\:{equation}\:\right) \\ $$

Question Number 175967 Answers: 0 Comments: 0

lim_(n→∞) [tan𝚿+(1/2)tan(𝚿/2)+(1/2^2 )tan(𝚿/2^2 )+...+(1/2^n )tan(𝚿/2^n )]

$$\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\:\left[\boldsymbol{\mathrm{tan}\Psi}+\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\mathrm{2}} }+...+\frac{\mathrm{1}}{\mathrm{2}^{\boldsymbol{{n}}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\boldsymbol{{n}}} }\right]\:\:\:\:\: \\ $$

Question Number 175961 Answers: 1 Comments: 0

Given that ((2tan15^0 )/(1+tan^2 15^0 ))=sin30^0 , find tan15^0 leaving the answer in surd form (radicals)

$$\mathrm{Given}\:\mathrm{that}\:\frac{\mathrm{2tan15}^{\mathrm{0}} }{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \mathrm{15}^{\mathrm{0}} }=\mathrm{sin30}^{\mathrm{0}} ,\:\mathrm{find}\:\mathrm{tan15}^{\mathrm{0}} \\ $$$$\mathrm{leaving}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form}\:\left(\mathrm{radicals}\right) \\ $$

Question Number 175959 Answers: 3 Comments: 2

f(x) = x^6 − 100x^5 + 100x^4 − 100x^3 + 100x^2 − 100x + 100 f(99) = ?

$${f}\left({x}\right)\:=\:{x}^{\mathrm{6}} \:−\:\mathrm{100}{x}^{\mathrm{5}} \:+\:\mathrm{100}{x}^{\mathrm{4}} \:−\:\mathrm{100}{x}^{\mathrm{3}} \:+\:\mathrm{100}{x}^{\mathrm{2}} \:−\:\mathrm{100}{x}\:+\:\mathrm{100} \\ $$$${f}\left(\mathrm{99}\right)\:=\:? \\ $$

Question Number 175956 Answers: 1 Comments: 1

Question Number 175954 Answers: 0 Comments: 0

Question Number 175953 Answers: 1 Comments: 0

Question Number 175952 Answers: 0 Comments: 0

If f(x)= csc (((πx)/3))+sec (((πx)/6)) and f ′(a)= −(π/9). Find the value of a.

$$\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{csc}\:\left(\frac{\pi\mathrm{x}}{\mathrm{3}}\right)+\mathrm{sec}\:\left(\frac{\pi\mathrm{x}}{\mathrm{6}}\right) \\ $$$$\:\mathrm{and}\:\mathrm{f}\:'\left(\mathrm{a}\right)=\:−\frac{\pi}{\mathrm{9}}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{a}. \\ $$

Question Number 175951 Answers: 0 Comments: 1

Given f(x)=ax^3 +bx^2 +cx+d a≠ 0 and ∣f ′(x)∣ ≤ 1 for 0≤x≤1 find max value of a.

$$\:{Given}\:{f}\left({x}\right)={ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}\: \\ $$$$\:{a}\neq\:\mathrm{0}\:{and}\:\mid{f}\:'\left({x}\right)\mid\:\leqslant\:\mathrm{1}\:{for}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\: \\ $$$$\:{find}\:{max}\:{value}\:{of}\:{a}. \\ $$

Question Number 175949 Answers: 1 Comments: 1

Question Number 175943 Answers: 1 Comments: 0

(1) ∃x∈R, x^2 +x+a=0. find the range of a. (2) ∀x∈R, x^2 +x+a=0. find the range of a.

$$\left(\mathrm{1}\right)\:\exists{x}\in\mathbb{R},\:{x}^{\mathrm{2}} +{x}+{a}=\mathrm{0}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$$$\left(\mathrm{2}\right)\:\forall{x}\in\mathbb{R},\:{x}^{\mathrm{2}} +{x}+{a}=\mathrm{0}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$

Question Number 175938 Answers: 2 Comments: 0

Question Number 175937 Answers: 1 Comments: 0

if y(x−y)^2 =x, then ∫(dx/(x−3y))=?

$${if}\:{y}\left({x}−{y}\right)^{\mathrm{2}} ={x},\:\:\:{then}\:\int\frac{{dx}}{{x}−\mathrm{3}{y}}=? \\ $$

Question Number 175923 Answers: 1 Comments: 0

what are the differences among “ if ”, “ only if ” and “ if and only if ”?

$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{differences}\:\mathrm{among}\:``\:{if}\:'',\:``\:{only}\:\:{if}\:''\:\mathrm{and}\:``\:{if}\:\:{and}\:\:{only}\:\:{if}\:''? \\ $$

Question Number 175925 Answers: 1 Comments: 1

1^x +6^x +8^x =9^x find x ? Mastermind

$$\mathrm{1}^{\mathrm{x}} +\mathrm{6}^{\mathrm{x}} +\mathrm{8}^{\mathrm{x}} =\mathrm{9}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 175916 Answers: 1 Comments: 1

f(x)= 2^( (( sin(x) +(√3) cos(x)))^(1/3) ) − 2^( ((−sin(x) −(√3) cos(x)))^(1/3) ) R_( f) =?

$$ \\ $$$$\:\:\:\:{f}\left({x}\right)=\:\mathrm{2}^{\:\sqrt[{\mathrm{3}}]{\:{sin}\left({x}\right)\:+\sqrt{\mathrm{3}}\:{cos}\left({x}\right)}\:} −\:\mathrm{2}^{\:\sqrt[{\mathrm{3}}]{−{sin}\left({x}\right)\:−\sqrt{\mathrm{3}}\:{cos}\left({x}\right)}} \\ $$$$\:\:\:\:\:\:\:{R}_{\:{f}} \:=? \\ $$

Question Number 175904 Answers: 2 Comments: 1

If 1 + sinx + sin^2 x + sin^3 x + ........ ∞ = 4 + 2(√3), x = ?

$$ \\ $$$$\mathrm{If}\:\:\mathrm{1}\:+\:{sinx}\:+\:{sin}^{\mathrm{2}} {x}\:+\:{sin}^{\mathrm{3}} {x}\:+\:........\:\infty\:\:\:=\:\:\mathrm{4}\:+\:\mathrm{2}\sqrt{\mathrm{3}},\: \\ $$$${x}\:=\:? \\ $$

Question Number 175901 Answers: 2 Comments: 1

Question Number 175894 Answers: 1 Comments: 0

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