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AllQuestion and Answers: Page 267

Question Number 188147 Answers: 3 Comments: 0

Question Number 188151 Answers: 1 Comments: 0

Simplify: (√(1+(1/1^2 )+(1/2^2 ))) +(√(1+(1/2^2 )+(1/3^2 ))) +...+(√(1+(1/(2022^2 ))+(1/(2023^2 ))))

$$\mathrm{Simplify}: \\ $$$$\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }}\:+\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }}\:+...+\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2022}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2023}^{\mathrm{2}} }} \\ $$

Question Number 188128 Answers: 1 Comments: 0

Question Number 188126 Answers: 0 Comments: 0

In convex polygon ABCD AB = 10 (√6) , CD = 18 ∠ ABD = 60° , ∠ BDC = 45° and BD = 13 (√6) + 9 (√2) find AC = ?

$$\mathrm{In}\:\mathrm{convex}\:\mathrm{polygon}\:\:\mathrm{ABCD} \\ $$$$\mathrm{AB}\:=\:\mathrm{10}\:\sqrt{\mathrm{6}}\:\:,\:\:\mathrm{CD}\:=\:\mathrm{18} \\ $$$$\angle\:\mathrm{ABD}\:=\:\mathrm{60}°\:\:,\:\:\angle\:\mathrm{BDC}\:=\:\mathrm{45}° \\ $$$$\mathrm{and}\:\:\mathrm{BD}\:=\:\mathrm{13}\:\sqrt{\mathrm{6}}\:+\:\mathrm{9}\:\sqrt{\mathrm{2}} \\ $$$$\mathrm{find}\:\:\mathrm{AC}\:=\:? \\ $$

Question Number 188119 Answers: 1 Comments: 1

Question Number 188107 Answers: 2 Comments: 0

Question Number 188100 Answers: 2 Comments: 0

Question Number 188098 Answers: 1 Comments: 0

∫x!dx

$$\int\boldsymbol{\mathrm{x}}!\boldsymbol{\mathrm{dx}} \\ $$

Question Number 188095 Answers: 2 Comments: 4

Question Number 188094 Answers: 0 Comments: 1

Question Number 188092 Answers: 0 Comments: 0

Question Number 188086 Answers: 1 Comments: 0

I = ∫_0 ^∞ ((tan^(−1) (x/a))/(x(x^2 +b^2 )))dx

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{I}\:\:\:=\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{tan}^{−\mathrm{1}} \left({x}/{a}\right)}{{x}\left({x}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)}{dx} \\ $$

Question Number 188083 Answers: 1 Comments: 3

determine the value of b for which y=((−x)/3) +b meets the graph of y^2 =x^3 orthogonally

$${determine}\:{the}\:{value}\:{of}\:{b}\:{for}\:{which}\: \\ $$$$\:\:\:{y}=\frac{−{x}}{\mathrm{3}}\:+{b}\:\:{meets}\:{the}\:{graph}\:{of} \\ $$$$\:{y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:\:{orthogonally} \\ $$

Question Number 188082 Answers: 1 Comments: 0

P(x) is a polynomial If P(x^2 + 1) = 6x^4 − x^2 + 5 Find P(x^2 − 1) = ?

$$\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial} \\ $$$$\mathrm{If}\:\:\:\mathrm{P}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:=\:\mathrm{6x}^{\mathrm{4}} \:−\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{5} \\ $$$$\mathrm{Find}\:\:\:\mathrm{P}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{1}\right)\:=\:? \\ $$

Question Number 188079 Answers: 0 Comments: 2

Question Number 188078 Answers: 2 Comments: 0

Question Number 188073 Answers: 2 Comments: 0

If x = (√((1 + (√5))/( (√5) − 1))) find 5x^2 −5x−1=?

$$\mathrm{If}\:\:\:\mathrm{x}\:=\:\sqrt{\frac{\mathrm{1}\:+\:\sqrt{\mathrm{5}}}{\:\sqrt{\mathrm{5}}\:−\:\mathrm{1}}}\:\:\:\:\:\mathrm{find}\:\:\:\:\mathrm{5x}^{\mathrm{2}} −\mathrm{5x}−\mathrm{1}=? \\ $$

Question Number 188072 Answers: 0 Comments: 0

If x_1 =−1 and x_(n+1) = (1 + (2/n))x_n + (4/n) Find x_(2023) = ?

$$\mathrm{If}\:\:\:\mathrm{x}_{\mathrm{1}} =−\mathrm{1}\:\:\:\mathrm{and}\:\:\:\mathrm{x}_{\boldsymbol{\mathrm{n}}+\mathrm{1}} =\:\left(\mathrm{1}\:+\:\frac{\mathrm{2}}{\mathrm{n}}\right)\mathrm{x}_{\boldsymbol{\mathrm{n}}} +\:\frac{\mathrm{4}}{\mathrm{n}} \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{x}_{\mathrm{2023}} \:=\:? \\ $$

Question Number 188071 Answers: 0 Comments: 1

If ((sin^4 x)/5) + ((cos^4 x)/7) = (1/(12)) Find ((sin^2 2x)/5) + ((cos^2 2x)/7) = ?

$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{sin}^{\mathrm{4}} \mathrm{x}}{\mathrm{5}}\:+\:\frac{\mathrm{cos}^{\mathrm{4}} \mathrm{x}}{\mathrm{7}}\:=\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\mathrm{Find}\:\:\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \:\mathrm{2x}}{\mathrm{5}}\:+\:\frac{\mathrm{cos}^{\mathrm{2}} \:\mathrm{2x}}{\mathrm{7}}\:=\:? \\ $$

Question Number 188069 Answers: 0 Comments: 1

how is solution ∫(√e^x )ln (√e^x )dx=?

$${how}\:{is}\:{solution} \\ $$$$\int\sqrt{{e}^{{x}} }\mathrm{ln}\:\sqrt{{e}^{{x}} }{dx}=? \\ $$

Question Number 188062 Answers: 1 Comments: 8

Question Number 188060 Answers: 4 Comments: 0

Question Number 188059 Answers: 1 Comments: 0

Question Number 188037 Answers: 1 Comments: 0

find (dy/dx) y=2x^(√x)

$${find}\:\frac{{dy}}{{dx}} \\ $$$${y}=\mathrm{2}{x}^{\sqrt{{x}}} \\ $$

Question Number 188036 Answers: 1 Comments: 0

∫2^x e^x dx

$$\int\mathrm{2}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 188035 Answers: 1 Comments: 0

solve ∫(x^2 /((a+bx)^2 ))dx

$${solve} \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}\right)^{\mathrm{2}} }{dx} \\ $$

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