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AllQuestion and Answers: Page 353

Question Number 179510 Answers: 1 Comments: 2

Evaluate ∫e^(4x) (√((1/e^(−2x) )+1)) dx

$${Evaluate}\:\int{e}^{\mathrm{4}{x}} \:\sqrt{\frac{\mathrm{1}}{{e}^{−\mathrm{2}{x}} }+\mathrm{1}}\:{dx} \\ $$

Question Number 179503 Answers: 0 Comments: 1

lim_(x→1) ((1/(tan^(−1) (x)−(π/4))) −(2/(x−1))) =?

$$\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)−\frac{\pi}{\mathrm{4}}}\:−\frac{\mathrm{2}}{\mathrm{x}−\mathrm{1}}\right)\:=? \\ $$

Question Number 179501 Answers: 1 Comments: 3

Question Number 179496 Answers: 1 Comments: 0

Evaluer ∫_1 ^2 ((sin (log(x)))/x)dx

$${Evaluer} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\mathrm{sin}\:\left(\mathrm{log}\left(\mathrm{x}\right)\right)}{\mathrm{x}}\mathrm{dx} \\ $$

Question Number 179494 Answers: 1 Comments: 0

Evaluer ∫((1−logx)/(1+x))dx

$${Evaluer} \\ $$$$\int\frac{\mathrm{1}−\mathrm{logx}}{\mathrm{1}+\mathrm{x}}\mathrm{dx} \\ $$

Question Number 179482 Answers: 3 Comments: 1

Question Number 179478 Answers: 3 Comments: 0

Find ∫_( 0) ^( (1/6)) (1/(x^(−5) (36x^2 +1)^(3/2) )) dx

$${Find}\:\int_{\:\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{6}}} \:\frac{\mathrm{1}}{{x}^{−\mathrm{5}} \:\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx} \\ $$

Question Number 179458 Answers: 1 Comments: 2

Find the area of the triangle in the first quadrant between the x and y axis and the tangent to the relationship curve y=(5/x)−(x/5) and x dont equal 0 at (0,5)

$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{quadrant}\:\mathrm{between}\:\mathrm{the}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{relationship}\:\mathrm{curve}\:\mathrm{y}=\frac{\mathrm{5}}{\mathrm{x}}−\frac{\mathrm{x}}{\mathrm{5}}\:\mathrm{and}\:\mathrm{x}\:\mathrm{dont} \\ $$$$\mathrm{equal}\:\mathrm{0}\:\mathrm{at}\:\left(\mathrm{0},\mathrm{5}\right) \\ $$

Question Number 179453 Answers: 1 Comments: 0

Question Number 179449 Answers: 2 Comments: 0

Solve for real numbers: 3sinx + 4(y + cosx) = y^2 + 9

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{3sinx}\:+\:\mathrm{4}\left(\mathrm{y}\:+\:\mathrm{cosx}\right)\:=\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{9} \\ $$

Question Number 179440 Answers: 0 Comments: 5

Question Number 179436 Answers: 2 Comments: 1

f(x) = (1/x) and g(x) = ((x + 2)/(2x + 1)) Find: g^(−1) (f(3)) = ?

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}\:+\:\mathrm{2}}{\mathrm{2x}\:+\:\mathrm{1}} \\ $$$$\mathrm{Find}:\:\:\:\:\:\mathrm{g}^{−\mathrm{1}} \left(\mathrm{f}\left(\mathrm{3}\right)\right)\:=\:? \\ $$

Question Number 179435 Answers: 1 Comments: 1

Question Number 179433 Answers: 0 Comments: 0

Question Number 179432 Answers: 2 Comments: 2

Question Number 179429 Answers: 0 Comments: 3

to tinku tara sir: for some reasons i don′t get any notifications about updates to my posts. can you please check sir? thank you!

$${to}\:{tinku}\:{tara}\:{sir}: \\ $$$${for}\:{some}\:{reasons}\:{i}\:{don}'{t}\:{get}\:{any} \\ $$$${notifications}\:{about}\:{updates}\:{to}\:{my} \\ $$$${posts}.\:{can}\:{you}\:{please}\:{check}\:{sir}?\: \\ $$$${thank}\:{you}! \\ $$

Question Number 179428 Answers: 1 Comments: 0

Find (dy/dx) if y = 3sin^2 (x−5x^2 )

$$\mathrm{Find}\:\:\frac{{dy}}{{dx}}\:\:\mathrm{if}\:\:{y}\:=\:\mathrm{3sin}^{\mathrm{2}} \left({x}−\mathrm{5}{x}^{\mathrm{2}} \right)\: \\ $$

Question Number 179420 Answers: 2 Comments: 4

a challening question: find the number of numbers which are divisible by 9 and consist of distinct digits.

$$\underline{{a}\:{challening}\:{question}:} \\ $$$${find}\:{the}\:{number}\:{of}\:{numbers}\:{which} \\ $$$${are}\:{divisible}\:{by}\:\mathrm{9}\:{and}\:{consist}\:{of} \\ $$$${distinct}\:{digits}. \\ $$

Question Number 179407 Answers: 0 Comments: 1

Study the relative position of the curve C_f with it asymptote; f(x)= x+ ((sin x)/x)

$${Study}\:{the}\:{relative}\:{position}\:{of}\:{the}\:{curve}\:{C}_{{f}} \:{with} \\ $$$$\:{it}\:{asymptote};\:{f}\left({x}\right)=\:{x}+\:\frac{\mathrm{sin}\:{x}}{{x}} \\ $$

Question Number 179405 Answers: 4 Comments: 0

Evaluate ∫ (dx/(x^4 (√(9−x^2 ))))

$$\:{Evaluate}\:\int\:\frac{{dx}}{{x}^{\mathrm{4}} \:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }} \\ $$

Question Number 179390 Answers: 1 Comments: 0

lim_(x→∞) (1−(5/( (√(x^3 −1)))))^(√(((x^2 +x+1)(4x−1))/4)) =?

$$\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}−\frac{\mathrm{5}}{\:\sqrt{{x}^{\mathrm{3}} −\mathrm{1}}}\right)^{\sqrt{\frac{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left(\mathrm{4}{x}−\mathrm{1}\right)}{\mathrm{4}}}} =? \\ $$

Question Number 179386 Answers: 2 Comments: 0

Question Number 179383 Answers: 3 Comments: 0

1• Evaluate I=∫ ((√(25x^2 −4))/x) dx 2• Find value of ∫_(2/5) ^( (4/5)) f(x) dx 3• Find value of ∫_(− (4/5)) ^( − (2/5)) f(x) dx

$$\mathrm{1}\bullet\:{Evaluate}\:{I}=\int\:\:\frac{\sqrt{\mathrm{25}{x}^{\mathrm{2}} −\mathrm{4}}}{{x}}\:{dx} \\ $$$$\:\mathrm{2}\bullet\:{Find}\:{value}\:{of}\:\int_{\frac{\mathrm{2}}{\mathrm{5}}} ^{\:\frac{\mathrm{4}}{\mathrm{5}}} {f}\left({x}\right)\:{dx} \\ $$$$\:\mathrm{3}\bullet\:{Find}\:{value}\:{of}\:\int_{−\:\frac{\mathrm{4}}{\mathrm{5}}} ^{\:−\:\frac{\mathrm{2}}{\mathrm{5}}} {f}\left({x}\right)\:{dx} \\ $$$$ \\ $$

Question Number 179371 Answers: 2 Comments: 2

Question Number 179369 Answers: 1 Comments: 0

Question Number 179366 Answers: 2 Comments: 5

lim_(x→π) ((sin(x/2)−1)/(x−π))=?

$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{{sin}\frac{{x}}{\mathrm{2}}−\mathrm{1}}{{x}−\pi}=? \\ $$

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