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Question Number 43128 Answers: 1 Comments: 5

Question Number 43036 Answers: 1 Comments: 1

Question Number 43031 Answers: 2 Comments: 2

Question Number 43027 Answers: 2 Comments: 1

Question Number 43023 Answers: 1 Comments: 1

Question Number 43011 Answers: 0 Comments: 2

Question Number 43008 Answers: 1 Comments: 0

(y′)^2 =−1+sin x y=?

$$\left({y}'\right)^{\mathrm{2}} =−\mathrm{1}+\mathrm{sin}\:{x} \\ $$$${y}=? \\ $$

Question Number 43007 Answers: 1 Comments: 1

calculate A_n =Σ_(k=0) ^n k C_n ^k B_n = Σ_(k=0) ^n k^2 C_n ^k C_n =Σ_(k=0) ^n k^3 C_n ^k

$${calculate}\: \\ $$$${A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:{C}_{{n}} ^{{k}} \\ $$$${B}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \\ $$$${C}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}^{\mathrm{3}} \:{C}_{{n}} ^{{k}} \\ $$

Question Number 43005 Answers: 0 Comments: 19

The base of triangle passes through a fixed point p(a,b) and its sides are respectively bisected at right angles by the line x+y=0 and x=9y if the locus of the third vartex is a circle. then find its equation.

$$\mathrm{The}\:\mathrm{base}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{passes}\:\mathrm{through} \\ $$$$\mathrm{a}\:\mathrm{fixed}\:\mathrm{point}\:\mathrm{p}\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{and}\:\mathrm{its}\:\mathrm{sides} \\ $$$$\mathrm{are}\:\mathrm{respectively}\:\mathrm{bisected}\:\mathrm{at}\:\mathrm{right}\:\mathrm{angles}\: \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}+\mathrm{y}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\mathrm{9y} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{third}\:\mathrm{vartex}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}. \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{its}\:\mathrm{equation}. \\ $$

Question Number 43003 Answers: 1 Comments: 0

let u_n = Σ_(1≤i<j≤n) (1/(√(ij))) 1) find a equivalent of u_n 2)calculate lim_(n→+∞) u_n

$${let}\:{u}_{{n}} =\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\frac{\mathrm{1}}{\sqrt{{ij}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} \:{u}_{{n}} \\ $$

Question Number 43001 Answers: 1 Comments: 0

prove that Π_(k=1) ^n (1+(1/k))>1+Σ_(k=1) ^n (1/k)

$${prove}\:{that}\:\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{\mathrm{1}}{{k}}\right)>\mathrm{1}+\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$

Question Number 43000 Answers: 2 Comments: 0

prove that (√(2+(√(2+....+(√2))))) =2cos((π/2^n ))

$${prove}\:{that}\:\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+....+\sqrt{\mathrm{2}}}}\:\:=\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right) \\ $$

Question Number 42999 Answers: 0 Comments: 1

let f(x)=(√x)+(1/(x−1)) 1) calculate f^((n)) (2) 2) if f(x) =Σ_(n=0) ^∞ a_n (x−2)^n find the sequence a_n

$${let}\:{f}\left({x}\right)=\sqrt{{x}}+\frac{\mathrm{1}}{{x}−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{if}\:{f}\left({x}\right)\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:{a}_{{n}} \left({x}−\mathrm{2}\right)^{{n}} \:{find}\:{the} \\ $$$${sequence}\:{a}_{{n}} \\ $$

Question Number 42995 Answers: 0 Comments: 0

Dear Jr inter students use this firmulas Derivates d/dx constant(k)=0 d/dx x^n =n.x^(n−1) d/dx x^2 =2x d/dx (√x) =1/2(√x) d/dx e^x =e^x d/dx a^x =a^x loxa d/dx logx =1/x _ d dx 1/x =−1/x^2

Question Number 42994 Answers: 0 Comments: 5

∫(√(1+((cos x)/(4tan x))))dx=?

$$\int\sqrt{\mathrm{1}+\frac{\mathrm{cos}\:{x}}{\mathrm{4tan}\:{x}}}{dx}=? \\ $$

Question Number 42988 Answers: 0 Comments: 0

reduce this matrix [(2,3,4,1),(1,7,2,3),((−1),4,2,0),(0,1,1,0) ]

$${reduce}\:{this}\:{matrix}\begin{bmatrix}{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{7}}&{\mathrm{2}}&{\mathrm{3}}\\{−\mathrm{1}}&{\mathrm{4}}&{\mathrm{2}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{0}}\end{bmatrix} \\ $$

Question Number 42948 Answers: 1 Comments: 5