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Question Number 199380 Answers: 0 Comments: 0

Question Number 199377 Answers: 1 Comments: 0

∫∫_R cos (max{x^3 , y^(3/2) })dx dy , where R = [0,1]×[0,1]

$$\:\:\int\underset{\mathrm{R}} {\int}\mathrm{cos}\:\left(\mathrm{max}\left\{\mathrm{x}^{\mathrm{3}} ,\:\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right\}\right)\mathrm{dx}\:\mathrm{dy}\:,\:\mathrm{where}\:\mathrm{R}\:=\:\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$

Question Number 199374 Answers: 3 Comments: 3

Question Number 199371 Answers: 0 Comments: 1

Question Number 199370 Answers: 0 Comments: 0

lim_(x→0) ((4e^(3x) −9e^(2x) +6x+5)/x^3 )=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}{e}^{\mathrm{3}{x}} −\mathrm{9}{e}^{\mathrm{2}{x}} +\mathrm{6}{x}+\mathrm{5}}{{x}^{\mathrm{3}} }=? \\ $$

Question Number 199369 Answers: 0 Comments: 0

∫_(−1) ^1 ∫_(−(√(1−x^2 ))) ^(√(1−x^2 )) ∫_(1−(√(1−x^2 −y^2 ))) ^(1+(√(1−y^2 ))) (x^2 +y^2 +z^2 )^(5/2) dx dy dz is

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \:\int_{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} ^{\mathrm{1}+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} {dx}\:{dy}\:{dz}\:\:{is} \\ $$

Question Number 199368 Answers: 2 Comments: 0

Question Number 199349 Answers: 0 Comments: 0

Question Number 199339 Answers: 1 Comments: 2

Question Number 199338 Answers: 2 Comments: 0

Question Number 199337 Answers: 1 Comments: 0

Question Number 199333 Answers: 2 Comments: 0

Find the number of integers greater than 6200 that can be formed from the digits 1,3,6,8 and 9, where each digit is used at most once.

$${Find}\:{the}\:{number}\:{of}\:{integers}\:{greater} \\ $$$${than}\:\mathrm{6200}\:{that}\:{can}\:{be}\:{formed}\:{from} \\ $$$${the}\:{digits}\:\mathrm{1},\mathrm{3},\mathrm{6},\mathrm{8}\:{and}\:\mathrm{9},\:{where}\:{each} \\ $$$${digit}\:{is}\:{used}\:{at}\:{most}\:{once}. \\ $$

Question Number 199331 Answers: 0 Comments: 0

What is the remainder when 1^1 +2^2 +3^3 +......+2023^(2023) is divided by 7

$${What}\:{is}\:{the}\:{remainder}\:{when} \\ $$$$\mathrm{1}^{\mathrm{1}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +......+\mathrm{2023}^{\mathrm{2023}} \:{is}\:{divided}\:{by}\:\mathrm{7} \\ $$

Question Number 199312 Answers: 0 Comments: 0

Determine the continuity ortherwise of the following functions a) ((7x^2 +x−3)/((x−2)^2 )) b) x^2 −4x+1 c) f(x) = {_(1 , x=1) ^(((4−x^2 )/(3−(√(x^2 −5)))) , x≠2)

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{continuity}\:\mathrm{ortherwise}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{following}\:\mathrm{functions} \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\:\frac{\mathrm{7x}^{\mathrm{2}} +\mathrm{x}−\mathrm{3}}{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{c}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\left\{_{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:,\:\:\:\:\:\mathrm{x}=\mathrm{1}} ^{\frac{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }{\mathrm{3}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{5}}}\:\:\:\:\:\:,\:\:\:\:\mathrm{x}\neq\mathrm{2}} \right. \\ $$

Question Number 199311 Answers: 2 Comments: 0

Find the number of positive integers that are factors of 3^(19) .7^(12) .10^(25) and are also multiples of 3^(15) .7^(10) .10^(19)

$${Find}\:{the}\:{number}\:{of}\:{positive}\:{integers} \\ $$$${that}\:{are}\:{factors}\:{of}\:\mathrm{3}^{\mathrm{19}} .\mathrm{7}^{\mathrm{12}} .\mathrm{10}^{\mathrm{25}} \:{and}\:{are} \\ $$$${also}\:{multiples}\:{of}\:\mathrm{3}^{\mathrm{15}} .\mathrm{7}^{\mathrm{10}} .\mathrm{10}^{\mathrm{19}} \\ $$

Question Number 199310 Answers: 1 Comments: 1

What is the probability that in a class of 18 people, there exists a group of 3 people born on the same day of the week?

$${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{a}\:{group}\:{of}\:\mathrm{3} \\ $$$${people}\:{born}\:{on}\:{the}\:{same}\:{day}\:{of}\:{the} \\ $$$${week}? \\ $$

Question Number 199309 Answers: 1 Comments: 0

a_(n+1 ) = a_n + (√(a_n ^2 + 1)) , a_0 = 0 find a_(n ) = ??

$$\:\:\:\:{a}_{{n}+\mathrm{1}\:} =\:{a}_{{n}} \:+\:\sqrt{{a}_{{n}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:\:,\:{a}_{\mathrm{0}} \:=\:\mathrm{0} \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{a}_{\mathrm{n}\:} \:=\:\:?? \\ $$

Question Number 199308 Answers: 0 Comments: 0

Question Number 199624 Answers: 0 Comments: 1

Question Number 203651 Answers: 3 Comments: 0

lim_(x→1) (2−x)^(tan(((πx)/2))) =?

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\mathrm{2}−{x}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{2}}\right)} =? \\ $$

Question Number 199290 Answers: 4 Comments: 1

If x=(√(p+iq))+(√(h+ik)) and (p/q)≠(k/h) then relate p,q,h,k ∈R such that x∈R.

$${If}\:{x}=\sqrt{{p}+{iq}}+\sqrt{{h}+{ik}} \\ $$$${and}\:\:\frac{{p}}{{q}}\neq\frac{{k}}{{h}}\:\:{then}\:{relate}\:{p},{q},{h},{k}\:\in\mathbb{R} \\ $$$${such}\:{that}\:{x}\in\mathbb{R}. \\ $$

Question Number 199286 Answers: 3 Comments: 0

Question Number 199261 Answers: 0 Comments: 0

Question Number 199259 Answers: 0 Comments: 1

Question Number 199621 Answers: 3 Comments: 0

Question Number 199620 Answers: 1 Comments: 0

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