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AllQuestion and Answers: Page 1407

Question Number 64017 Answers: 0 Comments: 4

why can′t we differentiate or intergrate powers of trigonometric functions such as 1) ∫cos^2 xdx? 3) ∫tan^2 2xdx 2)∫sin^2 xdx? 4) ∫sin^(10) x hence how do we solve such problems.?

$${why}\:{can}'{t}\:{we}\:{differentiate}\:{or}\:{intergrate}\:{powers}\:{of}\:{trigonometric} \\ $$$${functions}\:{such}\:{as}\: \\ $$$$\left.\mathrm{1}\left.\right)\:\int{cos}^{\mathrm{2}} {xdx}?\:\:\:\:\mathrm{3}\right)\:\int{tan}^{\mathrm{2}} \mathrm{2}{xdx} \\ $$$$\left.\mathrm{2}\left.\right)\int{sin}^{\mathrm{2}} {xdx}?\:\:\:\:\:\mathrm{4}\right)\:\int{sin}^{\mathrm{10}} {x} \\ $$$${hence}\:{how}\:{do}\:{we}\:{solve}\:{such}\:{problems}.? \\ $$

Question Number 64015 Answers: 1 Comments: 0

How can such questions be solved.? x^2 −∣7∣ +10=0 x^2 −∣x∣−6>0

$$\:{How}\:{can}\:{such}\:{questions}\:{be}\:{solved}.? \\ $$$$\:\:{x}^{\mathrm{2}} −\mid\mathrm{7}\mid\:+\mathrm{10}=\mathrm{0} \\ $$$$\:\:{x}^{\mathrm{2}} −\mid{x}\mid−\mathrm{6}>\mathrm{0} \\ $$$$\:\: \\ $$

Question Number 64012 Answers: 1 Comments: 0

Question Number 64011 Answers: 1 Comments: 3

lim_(x→0) ((x^x −1)/(xlnx))

$$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{x}^{\mathrm{x}} −\mathrm{1}}{\mathrm{xlnx}} \\ $$

Question Number 64009 Answers: 2 Comments: 1

Question Number 63985 Answers: 1 Comments: 0

Question Number 63984 Answers: 1 Comments: 5

is it true? e^(lnx) = x? if so then (d/dx)(e^(lnx) )=?

$${is}\:{it}\:{true}? \\ $$$$\:\:{e}^{{lnx}} =\:{x}? \\ $$$${if}\:{so}\:{then}\:\:\frac{{d}}{{dx}}\left({e}^{{lnx}} \right)=? \\ $$

Question Number 63983 Answers: 1 Comments: 0

Please i need someones help on this How do i find an Asymptote to a curve? and also how find a general solution for a differential equation.

$${Please}\:{i}\:{need}\:{someones}\:{help}\:{on}\:{this}\: \\ $$$${How}\:{do}\:{i}\:{find}\:{an}\:{Asymptote}\:{to}\:{a}\:{curve}? \\ $$$${and}\:{also}\:{how}\:{find}\:{a}\:{general}\:{solution}\:{for}\:{a}\:{differential}\: \\ $$$${equation}. \\ $$$$ \\ $$

Question Number 63981 Answers: 1 Comments: 0

Question Number 63976 Answers: 0 Comments: 3

∫secxdx ?

$$\int{secxdx}\:\:\:\:? \\ $$

Question Number 63975 Answers: 0 Comments: 0

Question Number 63964 Answers: 0 Comments: 2

lim_(x→+∞) e^(−xln(1−(1/x)))

$${li}\underset{{x}\rightarrow+\infty} {{m}e}^{−{xln}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right)} \\ $$

Question Number 63959 Answers: 0 Comments: 2

lim_(x→+∞) e^(xln(1+(1/x)))

$${li}\underset{{x}\rightarrow+\infty} {{m}e}^{{xln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)} \\ $$

Question Number 63958 Answers: 0 Comments: 1

x^6 −3x^5 +4x^4 −6x^3 +5x^2 −3x+2=0

$${x}^{\mathrm{6}} −\mathrm{3}{x}^{\mathrm{5}} +\mathrm{4}{x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}=\mathrm{0} \\ $$

Question Number 63957 Answers: 0 Comments: 0

f0f=θ

$${f}\mathrm{0}{f}=\theta \\ $$

Question Number 63956 Answers: 1 Comments: 0

x^2 −y^2 =24

$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{24} \\ $$

Question Number 63945 Answers: 0 Comments: 1

solve at Z^2 x^2 −2y^2 +xy +2 =0

$${solve}\:{at}\:{Z}^{\mathrm{2}} \:\:{x}^{\mathrm{2}} −\mathrm{2}{y}^{\mathrm{2}} \:+{xy}\:+\mathrm{2}\:=\mathrm{0} \\ $$

Question Number 63943 Answers: 1 Comments: 1

If x+y=1, then Σ_(r=0) ^n r ^n C_r x^r y^(n−r) equals

$$\mathrm{If}\:\:\:{x}+{y}=\mathrm{1},\:\mathrm{then}\:\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}\:\:^{{n}} {C}_{\mathrm{r}} \:{x}^{{r}} {y}^{{n}−{r}} \:\mathrm{equals} \\ $$

Question Number 63942 Answers: 1 Comments: 1

Let (1+x)^n = Σ_(r=0) ^n C_r x^r and Σ_(r=0) ^n (C_r /(r+1)) = k, then the value of k is

$$\mathrm{Let}\:\left(\mathrm{1}+{x}\right)^{{n}} =\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{C}_{{r}} \:{x}^{{r}} \:\mathrm{and}\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:\frac{{C}_{{r}} }{{r}+\mathrm{1}}\:=\:{k}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is} \\ $$

Question Number 63941 Answers: 1 Comments: 0

If the sum of the coefficients in the expansion of (1−3x+10x^2 )^n is a and if the sum of the coefficients in the expansion of (1+x^2 )^n is b, then

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{1}−\mathrm{3}{x}+\mathrm{10}{x}^{\mathrm{2}} \right)^{{n}} \:\mathrm{is}\:\:{a}\:\mathrm{and}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} \:\mathrm{is} \\ $$$${b},\:\mathrm{then} \\ $$

Question Number 63940 Answers: 1 Comments: 0

If the coefficient of (2r+4)th and (r−2)th terms in the expansion of (1+x)^(18) are equal, then the value of r is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\left(\mathrm{2}{r}+\mathrm{4}\right)\mathrm{th}\:\mathrm{and}\:\left({r}−\mathrm{2}\right)\mathrm{th} \\ $$$$\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{\mathrm{18}} \:\mathrm{are} \\ $$$$\mathrm{equal},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{r}\:\mathrm{is} \\ $$

Question Number 63939 Answers: 0 Comments: 0

If the (r+1)th term in the expansion of (((a/(√b)))^(1/3) + (√(b/(a)^(1/3) )))^(21) contains a and b to one and the same power, then the value of r is

$$\mathrm{If}\:\:\mathrm{the}\:\left({r}+\mathrm{1}\right)\mathrm{th}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\sqrt[{\mathrm{3}}]{\frac{{a}}{\sqrt{{b}}}}\:+\:\sqrt{\frac{{b}}{\sqrt[{\mathrm{3}}]{{a}}}}\right)^{\mathrm{21}} \:\mathrm{contains}\:{a}\:\mathrm{and}\:{b}\:\mathrm{to} \\ $$$$\mathrm{one}\:\mathrm{and}\:\mathrm{the}\:\mathrm{same}\:\mathrm{power},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{r}\:\mathrm{is} \\ $$

Question Number 63938 Answers: 0 Comments: 0

The number of terms in the expansion of (2x+3y−4z)^n is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{2}{x}+\mathrm{3}{y}−\mathrm{4}{z}\right)^{{n}} \:\mathrm{is} \\ $$

Question Number 63937 Answers: 1 Comments: 0

The coefficient of x^r in the expansion of (1−4x)^(−1/2) is

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{r}} \:\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}−\mathrm{4}{x}\right)^{−\mathrm{1}/\mathrm{2}} \:\:\mathrm{is} \\ $$

Question Number 63936 Answers: 0 Comments: 0

The coefficient of the term independent of x in the expansion of (1+x+2x^3 )((3/2) x^2 − (1/(3x)))^9 is

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{term}\:\mathrm{independent} \\ $$$$\mathrm{of}\:\:{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\: \\ $$$$\left(\mathrm{1}+{x}+\mathrm{2}{x}^{\mathrm{3}} \right)\left(\frac{\mathrm{3}}{\mathrm{2}}\:{x}^{\mathrm{2}} \:−\:\frac{\mathrm{1}}{\mathrm{3}{x}}\right)^{\mathrm{9}} \:\mathrm{is} \\ $$

Question Number 63935 Answers: 0 Comments: 0

If the 9^(th) term in the expansion of [3^(log_3 (√(25^(x−1) +7))) + 3^(− (1/8) log_3 (5^(x−1) +1)) ]^(10) is equal to 180 and x > 1, then x equals

$$\mathrm{If}\:\mathrm{the}\:\mathrm{9}^{\mathrm{th}} \mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left[\mathrm{3}^{\mathrm{log}_{\mathrm{3}} \:\sqrt{\mathrm{25}^{{x}−\mathrm{1}} +\mathrm{7}}} +\:\mathrm{3}^{−\:\frac{\mathrm{1}}{\mathrm{8}}\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{5}^{{x}−\mathrm{1}} +\mathrm{1}\right)} \right]^{\mathrm{10}} \:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{180}\:\mathrm{and}\:\:{x}\:>\:\mathrm{1},\:\mathrm{then}\:{x}\:\mathrm{equals} \\ $$

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