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AllQuestion and Answers: Page 1106

Question Number 106782 Answers: 1 Comments: 0

∫2xdx

Question Number 106779 Answers: 3 Comments: 0

^(≻bobhans≺) How do you find a point on the curve y=x^2 closest to the point (0,18) ?

$$\:\:\:\:\:\:\:\:\:^{\succ\mathrm{bobhans}\prec} \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{closest}\:\mathrm{to}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{0},\mathrm{18}\right)\:? \\ $$

Question Number 106775 Answers: 3 Comments: 0

^(@bemath@) (1) (d^2 y/dx^2 ) −6(dy/dx) + 9y = 1+x+x^2 (2) { ((x^3 +3y^3 = 11)),((x^2 y +xy^2 = 6)) :}

$$\:\:\:\:\:\:\:\:\:\:\:^{@\mathrm{bemath}@} \\ $$$$\:\left(\mathrm{1}\right)\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:−\mathrm{6}\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{9y}\:=\:\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} \\ $$$$\:\:\left(\mathrm{2}\right)\:\begin{cases}{\mathrm{x}^{\mathrm{3}} +\mathrm{3y}^{\mathrm{3}} \:=\:\mathrm{11}}\\{\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\mathrm{xy}^{\mathrm{2}} \:=\:\mathrm{6}}\end{cases}\: \\ $$

Question Number 106771 Answers: 2 Comments: 1

@bemath@ lim_(x→π) [((4(x−π) cos^2 x)/(π(π−2x) cos (x−(π/2))))]= ?

$$\:\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\left[\frac{\mathrm{4}\left(\mathrm{x}−\pi\right)\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}{\pi\left(\pi−\mathrm{2x}\right)\:\mathrm{cos}\:\left(\mathrm{x}−\frac{\pi}{\mathrm{2}}\right)}\right]=\:? \\ $$

Question Number 106745 Answers: 2 Comments: 8

Question Number 106744 Answers: 0 Comments: 3

∫ x^x^x^x dx

$$\int\:{x}^{{x}^{{x}^{{x}} } } {dx} \\ $$

Question Number 106743 Answers: 1 Comments: 0

∫(√(secy))dy

$$\int\sqrt{{secy}}{dy} \\ $$

Question Number 106730 Answers: 1 Comments: 0

Question Number 106727 Answers: 2 Comments: 0

Question Number 106726 Answers: 1 Comments: 0

Prove sin5θ=16sin^5 θ−20sin^3 θ+5sinθ Hence, show that sin 6° is an irrational number.

$$\mathrm{Prove}\:\mathrm{sin5}\theta=\mathrm{16sin}^{\mathrm{5}} \theta−\mathrm{20sin}^{\mathrm{3}} \theta+\mathrm{5sin}\theta \\ $$$$\mathrm{Hence},\:\mathrm{show}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{6}°\:\mathrm{is}\:\mathrm{an} \\ $$$$\mathrm{irrational}\:\mathrm{number}.\: \\ $$

Question Number 106774 Answers: 4 Comments: 0

^(@bemath@) (1) 3^x + 3^((√x) ) = 90. find x ? (2) x (dy/dx)−(1+x)y = xy^2

$$\:\:\:\:\overset{@\mathrm{bemath}@} {\:} \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\:\mathrm{3}^{{x}} \:+\:\mathrm{3}^{\sqrt{{x}}\:} =\:\mathrm{90}.\:\mathrm{find}\:{x}\:?\: \\ $$$$\:\:\left(\mathrm{2}\right)\:\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\left(\mathrm{1}+\mathrm{x}\right)\mathrm{y}\:=\:\mathrm{xy}^{\mathrm{2}} \\ $$

Question Number 106709 Answers: 3 Comments: 0

∫ ((sin^2 x dx)/(1−sin x cos x)) ?

$$ \\ $$$$\:\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}}{\mathrm{1}−\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}\:? \\ $$

Question Number 106707 Answers: 2 Comments: 0

@bemath@ Given { ((f(x)=2x+3)),(((g○f)(x)=2x−1)) :} find (f○g)(2).

$$\:\:\:\:@\mathrm{bemath}@ \\ $$$$\mathcal{G}\mathrm{iven}\:\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{3}}\\{\left(\mathrm{g}\circ\mathrm{f}\right)\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1}}\end{cases} \\ $$$$\mathrm{find}\:\left(\mathrm{f}\circ\mathrm{g}\right)\left(\mathrm{2}\right). \\ $$

Question Number 106705 Answers: 1 Comments: 0

@bemath@ ∫ ((1+x^2 )/(√(9−4x^2 ))) dx

$$\:\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\:\:\:\:\:\int\:\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\sqrt{\mathrm{9}−\mathrm{4x}^{\mathrm{2}} }}\:\mathrm{dx}\: \\ $$

Question Number 106695 Answers: 1 Comments: 0

#bobhans# 3^x −2^(x+1) ≤ (√(2.9^x −10.6^x +2^(2x+3) )) find the solution set

$$\:\:\:\:#\mathrm{bobhans}# \\ $$$$\mathrm{3}^{\mathrm{x}} −\mathrm{2}^{\mathrm{x}+\mathrm{1}} \:\leqslant\:\sqrt{\mathrm{2}.\mathrm{9}^{\mathrm{x}} −\mathrm{10}.\mathrm{6}^{\mathrm{x}} +\mathrm{2}^{\mathrm{2x}+\mathrm{3}} } \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set} \\ $$

Question Number 106694 Answers: 3 Comments: 0

Question Number 106691 Answers: 2 Comments: 0

determine using laplce transformation this integrale ∫_0 ^(+∞) ((tsin(tx))/(a^2 +t^(2 ) ))dt

$$\boldsymbol{{determine}}\:\boldsymbol{{using}}\:\:\boldsymbol{{laplce}}\:\boldsymbol{{transformation}}\:\boldsymbol{{this}} \\ $$$$\boldsymbol{{integrale}}\: \\ $$$$\:\:\int_{\mathrm{0}} ^{+\infty} \frac{\boldsymbol{{tsin}}\left(\boldsymbol{{tx}}\right)}{\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{t}}^{\mathrm{2}\:} }\boldsymbol{{dt}} \\ $$

Question Number 106690 Answers: 1 Comments: 0

this question was repeatd six times in a various exams between 1971 to 2001. if C_0 ,C_1 ,C_2 .......,C_n are the coefficients in the expansion of (1+x)^n then c_0 +2C_1 +3C_2 ........(n+1)C_n =?

$${this}\:{question}\:{was}\:{repeatd}\:{six}\:{times} \\ $$$${in}\:{a}\:{various}\:{exams}\:{between}\:\mathrm{1971}\:{to}\:\mathrm{2001}. \\ $$$${if}\:{C}_{\mathrm{0}} ,{C}_{\mathrm{1}} ,{C}_{\mathrm{2}} .......,{C}_{{n}} \:{are}\:{the}\:{coefficients} \\ $$$${in}\:{the}\:{expansion}\:{of}\:\left(\mathrm{1}+{x}\right)^{{n}} \:{then} \\ $$$${c}_{\mathrm{0}} +\mathrm{2}{C}_{\mathrm{1}} +\mathrm{3}{C}_{\mathrm{2}} ........\left({n}+\mathrm{1}\right){C}_{{n}} =? \\ $$

Question Number 106688 Answers: 0 Comments: 0

Σ_(k=0) ^∞ (((−1)^n )/((2n+1)!))z^(2n−14) =?

$$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!}{z}^{\mathrm{2}{n}−\mathrm{14}} =? \\ $$

Question Number 106683 Answers: 0 Comments: 0

Prove that ∫_0 ^π ln(1−2αcost+α^2 )dt=2πlnα

$$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\pi} \mathrm{ln}\left(\mathrm{1}−\mathrm{2}\alpha\mathrm{cost}+\alpha^{\mathrm{2}} \right)\mathrm{dt}=\mathrm{2}\pi\mathrm{ln}\alpha \\ $$

Question Number 106677 Answers: 3 Comments: 0

Question Number 106666 Answers: 2 Comments: 2

In 2x+3y=8 and 5x+Ky=3, find the value of K so that the given system of equation has infinte solution.

$$\mathrm{In}\:\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{8}\:\mathrm{and}\:\:\mathrm{5}{x}+{Ky}=\mathrm{3},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{K}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{given}\:\mathrm{system} \\ $$$$\mathrm{of}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{infinte}\:\mathrm{solution}. \\ $$

Question Number 106665 Answers: 1 Comments: 0

Find a fourth proportional to 3, 12 and 15

$$\:\mathrm{Find}\:\mathrm{a}\:\mathrm{fourth}\:\mathrm{proportional}\:\mathrm{to} \\ $$$$\:\mathrm{3},\:\mathrm{12}\:\mathrm{and}\:\mathrm{15} \\ $$

Question Number 106664 Answers: 3 Comments: 0

Factorise: x^6 + 64y^6

$$\mathrm{Factorise}:\:\:\:{x}^{\mathrm{6}} \:+\:\mathrm{64}{y}^{\mathrm{6}} \\ $$

Question Number 106663 Answers: 2 Comments: 0

Question Number 106662 Answers: 1 Comments: 0

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