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Question Number 11648 Answers: 1 Comments: 0

∣x∣<l Σ_(n=1) ^∞ x^n =?

$$\mid\mathrm{x}\mid<\mathrm{l} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{x}^{\mathrm{n}} =? \\ $$

Question Number 11633 Answers: 1 Comments: 0

A geometric sequence with n terms a_1 , a_2 , a_3 , ..., a_n which has a_1 . a_n = 3 If the product of all n terms = a_1 a_2 a_3 ...a_n = 59049 Determine the value of n

$$\mathrm{A}\:\mathrm{geometric}\:\mathrm{sequence}\:\mathrm{with}\:{n}\:\mathrm{terms}\: \\ $$$${a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:...,\:{a}_{{n}} \:\mathrm{which}\:\mathrm{has}\:{a}_{\mathrm{1}} \:.\:{a}_{{n}} \:=\:\mathrm{3} \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:{n}\:\mathrm{terms}\:=\:{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}} ...{a}_{{n}} =\:\mathrm{59049} \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{n} \\ $$

Question Number 11632 Answers: 1 Comments: 0

Question Number 11628 Answers: 1 Comments: 0

p(x−1)+p(x+1)=4x^2 −2x+10 p(x)=?

$$\mathrm{p}\left(\mathrm{x}−\mathrm{1}\right)+\mathrm{p}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{4x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{10} \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=? \\ $$

Question Number 11621 Answers: 1 Comments: 0

Evaluate ∫((ax+b)/(cx+d))dx

$${Evaluate}\:\:\int\frac{{ax}+{b}}{{cx}+{d}}{dx} \\ $$

Question Number 11619 Answers: 1 Comments: 1

Evaluate ∫(dx/((x+a)(x+b)))

$${Evaluate}\:\int\frac{{dx}}{\left({x}+{a}\right)\left({x}+{b}\right)} \\ $$

Question Number 11616 Answers: 3 Comments: 0

EvAluate ∫(x^2 +9)^9 dx

$${EvAluate}\:\int\left({x}^{\mathrm{2}} +\mathrm{9}\right)^{\mathrm{9}} {dx} \\ $$

Question Number 11613 Answers: 0 Comments: 0

Can you evaluate the equation of a Ellipse?

$${Can}\:{you}\:{evaluate}\:{the}\:{equation}\:{of} \\ $$$${a}\:{Ellipse}? \\ $$

Question Number 11611 Answers: 0 Comments: 0

Can you prove the Taylor′s series without using mean value theorem?

$${Can}\:{you}\:{prove}\:{the}\:{Taylor}'{s}\:{series}\: \\ $$$${without}\:{using}\:{mean}\:{value}\:{theorem}? \\ $$$$ \\ $$

Question Number 11609 Answers: 1 Comments: 3

Evaluate ∫x^x dx

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

Question Number 11608 Answers: 1 Comments: 0

If f(x)=xtan^(−1) ((1/x)) , x≠0 =0 , x=0 show that f is countinous but not differentiable at x=0.

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{xtan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:,\:\:\:\:\:\:\:\mathrm{x}\neq\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}\:,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{0} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{f}\:\mathrm{is}\:\mathrm{countinous}\:\mathrm{but}\:\mathrm{not}\:\mathrm{differentiable} \\ $$$$\mathrm{at}\:\mathrm{x}=\mathrm{0}. \\ $$

Question Number 11607 Answers: 1 Comments: 0

A parabola with equation y = (x^2 /k) − 5 intersects a circle with equation x^2 + y^2 = 25 at exactly 3 points A, B, C Determine all such positive integers k for which the area of ΔABC is an integer

$$\mathrm{A}\:\mathrm{parabola}\:\mathrm{with}\:\mathrm{equation}\:{y}\:=\:\frac{{x}^{\mathrm{2}} }{{k}}\:−\:\mathrm{5}\:\mathrm{intersects} \\ $$$$\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:\mathrm{25}\:\mathrm{at}\:\mathrm{exactly}\:\mathrm{3}\:\mathrm{points}\:{A},\:{B},\:{C} \\ $$$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{such}\:\mathrm{positive}\:\mathrm{integers}\:{k}\:\mathrm{for}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer} \\ $$

Question Number 11606 Answers: 1 Comments: 0

What is the smallest positive integer x for which (1/(32)) = (x/(10^y )) for some positive integer y ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer}\:{x}\:\mathrm{for} \\ $$$$\mathrm{which}\:\frac{\mathrm{1}}{\mathrm{32}}\:=\:\frac{{x}}{\mathrm{10}^{{y}} }\:\:\mathrm{for}\:\mathrm{some}\:\mathrm{positive}\:\mathrm{integer}\:{y}\:? \\ $$

Question Number 11600 Answers: 1 Comments: 0

A number is selected at random from the integers 1 to 100 exclusive, What is the chance of choosing at random a two digit number which is (a) Divisible by 4 (b) The multiple of 5

Question Number 11599 Answers: 1 Comments: 0

A number is selected at random from the integers 10 to 35 exclussive, such that the chances take the subsets of P, Q and R respectively, where P is even , Q is even or prime number, and R is odd prime numbers. What is the probability (a) That exacly one of the events of the subset is choosen ? (b) Of choosen at most two of the subset of the event.

Question Number 11597 Answers: 1 Comments: 0

y = x^x^(√x) , find (dy/dx)

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

Question Number 11594 Answers: 1 Comments: 0

please how can demonstred sin(2x)_ /cos(2x)=2sin(2x)

$${please}\:{how}\:{can}\:{demonstred}\: \\ $$$${sin}\left(\mathrm{2}{x}\underset{} {\right)}/{cos}\left(\mathrm{2}{x}\right)=\mathrm{2}{sin}\left(\mathrm{2}{x}\right) \\ $$

Question Number 11591 Answers: 1 Comments: 0

what is the intercept of (x^2 /a^2 )−(y^2 /b^2 )=1 on the x-axis ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{intercept}\:\mathrm{of}\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }−\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1}\:\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{x}-\mathrm{axis}\:? \\ $$

Question Number 11581 Answers: 2 Comments: 0

cAn you prove the chAin role??

$${cAn}\:{you}\:{prove}\:{the}\:{chAin}\:{role}?? \\ $$