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AllQuestion and Answers: Page 1142

Question Number 103585 Answers: 1 Comments: 0

Question Number 103582 Answers: 0 Comments: 3

Question Number 103574 Answers: 0 Comments: 0

Question Number 103721 Answers: 2 Comments: 0

∫_0 ^∞ ((cosx)/(x^2 +1))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{cosx}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 103563 Answers: 2 Comments: 0

find laplase transform of the function f(t)=sin^2 t cos^3 t ?

$${find}\:{laplase}\:{transform}\:{of}\:{the}\:{function} \\ $$$${f}\left({t}\right)={sin}^{\mathrm{2}} {t}\:\:{cos}^{\mathrm{3}} {t}\:\:? \\ $$

Question Number 103560 Answers: 3 Comments: 1

S=Σ_(k=1) ^(17) k∙2^k =?

$$\mathrm{S}=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{17}} {\sum}}\mathrm{k}\centerdot\mathrm{2}^{\mathrm{k}} =? \\ $$

Question Number 103553 Answers: 3 Comments: 0

Question Number 103515 Answers: 1 Comments: 0

given f(x) = f(x+(π/6)) ∀x∈R if ∫_0 ^(π/6) f(x)dx = T then ∫_π ^(7π/3) f(x+π) dx ?

$${given}\:{f}\left({x}\right)\:=\:{f}\left({x}+\frac{\pi}{\mathrm{6}}\right)\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{6}} {\int}}{f}\left({x}\right){dx}\:=\:{T}\:{then}\:\underset{\pi} {\overset{\mathrm{7}\pi/\mathrm{3}} {\int}}{f}\left({x}+\pi\right) \\ $$$${dx}\:? \\ $$

Question Number 103513 Answers: 2 Comments: 0

coefficient of x^5 in expansion (1+x^2 )^5 (1+x)^4 equal to (a) 40 (b) 45 (c) 50 (d) 55 (e) 60

$${coefficient}\:{of}\:{x}^{\mathrm{5}} \:{in}\:{expansion} \\ $$$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{5}} \left(\mathrm{1}+{x}\right)^{\mathrm{4}} \:{equal}\:{to}\: \\ $$$$\left({a}\right)\:\mathrm{40}\:\:\:\:\:\:\left({b}\right)\:\mathrm{45}\:\:\:\:\:\left({c}\right)\:\mathrm{50}\:\:\:\:\left({d}\right)\:\mathrm{55} \\ $$$$\left({e}\right)\:\mathrm{60} \\ $$

Question Number 103512 Answers: 2 Comments: 2

∫ ((x dx)/((cot x+tan x)^2 )) = (a) (x/(16))−((x sin 4x)/(32))−((cos 4x)/(128))+c (b) (x/(16))+((x sin 4x)/(32))−((cos 4x)/(128))+c (c) (x/(16))+((xsin 4x)/(64))+((cos 4x)/(128))+c (d)(x/(16))+((xcos 4x)/(32))+((sin 4x)/(128))+c

Question Number 103511 Answers: 1 Comments: 1

∫ (dx/((√x) ((x)^(1/4) +1))) =__ (a) −((9 (x)^(1/4) +1)/(18((x)^(1/4) +1)^9 )) + c (b) ((9 (x)^(1/4) +1)/(18((x)^(1/4) +1)^9 )) +c (c) −((9 (x)^(1/4) −1)/(18((x)^(1/4) +1)^9 )) +c (d) ((9 (x)^(1/4) +1)/(8((x)^(1/4) +1)^9 )) + c

Question Number 103510 Answers: 1 Comments: 5

Question Number 103504 Answers: 0 Comments: 0

Question Number 103503 Answers: 2 Comments: 0

Solve : 3^x = 4x

$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:{Solve}\:: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{3}^{{x}} \:=\:\mathrm{4}{x} \\ $$

Question Number 103497 Answers: 0 Comments: 0

Question Number 103655 Answers: 0 Comments: 3

lim_(x→∞) (−ln((10)/(17)))^(((17)/(10))x) =???

$${li}\underset{{x}\rightarrow\infty} {{m}}\left(−{ln}\frac{\mathrm{10}}{\mathrm{17}}\right)^{\frac{\mathrm{17}}{\mathrm{10}}{x}} =??? \\ $$

Question Number 103654 Answers: 1 Comments: 0

if a,b>1 lim_(x→0^+ ) ((ln(b−x))/(ax))=???

$$\:{if}\:{a},{b}>\mathrm{1}\:\:{li}\underset{{x}\rightarrow\mathrm{0}^{+} } {{m}}\frac{{ln}\left({b}−{x}\right)}{{ax}}=??? \\ $$

Question Number 103537 Answers: 1 Comments: 0

∫(x/((a^2 cosx+b^2 sinx)))dx

$$\int\frac{\mathrm{x}}{\left(\mathrm{a}^{\mathrm{2}} \mathrm{cosx}+\mathrm{b}^{\mathrm{2}} \mathrm{sinx}\right)}\mathrm{dx} \\ $$

Question Number 103492 Answers: 4 Comments: 1

Q1: Evaluate ∫_(−1) ^( 1) ∣x∣∙(x^3 +1)dx Q2: Find the sum of all integers k for which the equation 2x^3 −6x^2 +k=0 has more than one solution. Q3: Find the shortest distance from a point on the curve y=x^2 −x to the line y=x−3

$$\mathrm{Q1}:\:\:\mathrm{Evaluate}\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} \mid\mathrm{x}\mid\centerdot\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Q2}:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{integers}\:{k}\:\mathrm{for}\: \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{2}{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} +{k}=\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{more}\:\mathrm{than}\:\mathrm{one}\:\mathrm{solution}. \\ $$$$ \\ $$$$\mathrm{Q3}:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{a}\: \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:{y}={x}^{\mathrm{2}} −{x}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line} \\ $$$${y}={x}−\mathrm{3} \\ $$

Question Number 103489 Answers: 2 Comments: 0