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Question Number 44988    Answers: 1   Comments: 0

A tangent to ellipse (x^2 /a^(2 ) )+(y^2 /b^2 )=1 at point p meets the minor axis at L if the normal at p meets the major axis at m.find the locus of midpoint LM

$$\boldsymbol{\mathrm{A}}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{ellipse}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}\:} }+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{point}}\:\boldsymbol{\mathrm{p}}\:\boldsymbol{\mathrm{meets}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{minor}}\:\boldsymbol{\mathrm{axis}} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{L}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{normal}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{p}}\:\boldsymbol{\mathrm{meets}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{m}}.\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{locus}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{midpoint}}\:\boldsymbol{\mathrm{LM}} \\ $$

Question Number 44967    Answers: 1   Comments: 0

Question Number 44965    Answers: 0   Comments: 0

Find the sum of the nth term of the series: (1/(1.2.3)) + (1/(4.5.6)) + (1/(7.8.9)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:\:+\:...\: \\ $$

Question Number 44986    Answers: 1   Comments: 1

Find the sum of the nth term of the series: (1/(1.2.3)) + (1/(4.5.6)) + (1/(7.8.9)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:+\:... \\ $$

Question Number 44952    Answers: 0   Comments: 1

Question Number 44951    Answers: 1   Comments: 3

Question Number 44950    Answers: 1   Comments: 4

Question Number 44936    Answers: 0   Comments: 0

Question Number 44929    Answers: 2   Comments: 1

Question Number 44928    Answers: 0   Comments: 3

Question Number 44918    Answers: 2   Comments: 5

Find the sum to n terms of: (1/(1.2.3)) + (3/(2.3.4)) + (5/(3.4.5)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{3}}{\mathrm{2}.\mathrm{3}.\mathrm{4}}\:+\:\frac{\mathrm{5}}{\mathrm{3}.\mathrm{4}.\mathrm{5}}\:+\:...\: \\ $$

Question Number 44920    Answers: 2   Comments: 0

solve.3^(sin2x+2cos^2 x) +3^(1−sin2x+2sin^2 x) =28

$$\boldsymbol{\mathrm{solve}}.\mathrm{3}^{\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{2}\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} +\mathrm{3}^{\mathrm{1}−\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{2}\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} =\mathrm{28} \\ $$

Question Number 44921    Answers: 1   Comments: 1

∫(1/(1+ln x))=?

$$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{ln}\:\mathrm{x}}=? \\ $$

Question Number 44907    Answers: 0   Comments: 1

Question Number 44906    Answers: 0   Comments: 0

Question Number 44901    Answers: 0   Comments: 1

Question Number 44900    Answers: 1   Comments: 0

Question Number 44898    Answers: 1   Comments: 1

If x^4 +px^3 +qx^2 +rx+5 = 0 has four real roots, then find the minimum value of pr.

$${If}\:\:\:\:{x}^{\mathrm{4}} +{px}^{\mathrm{3}} +{qx}^{\mathrm{2}} +{rx}+\mathrm{5}\:=\:\mathrm{0} \\ $$$${has}\:{four}\:{real}\:{roots},\:{then}\:{find} \\ $$$$\:{the}\:{minimum}\:{value}\:{of}\:\boldsymbol{{pr}}. \\ $$

Question Number 44891    Answers: 1   Comments: 0

Question Number 44892    Answers: 1   Comments: 2

Find the formular for the sum of the first kth power of natural number

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{kth}\:\mathrm{power}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{number} \\ $$

Question Number 44876    Answers: 1   Comments: 0

Question Number 44874    Answers: 0   Comments: 2

Question Number 44872    Answers: 1   Comments: 1

Question Number 44858    Answers: 0   Comments: 0

Find the formular for the first kth power of natural numbers

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{kth}\:\mathrm{power}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{numbers} \\ $$

Question Number 44826    Answers: 2   Comments: 0

Let A and B be sets. Prove that A = B if and only if A ∪ B = A ∩ B

$$\mathrm{Let}\:{A}\:\mathrm{and}\:{B}\:\mathrm{be}\:\mathrm{sets}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{A}\:=\:{B}\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:{A}\:\cup\:{B}\:=\:{A}\:\cap\:{B} \\ $$

Question Number 44819    Answers: 0   Comments: 7

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