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Question Number 148860    Answers: 0   Comments: 0

f(x):= ∣ x^( 2) − (a+1)x +2a^( 2) −1∣ is differentiable on ( 1, 2 ). find the value(s) of ′ a ′ . ........

$$ \\ $$$$\:\:\:{f}\left({x}\right):=\:\mid\:{x}^{\:\mathrm{2}} −\:\left({a}+\mathrm{1}\right){x}\:+\mathrm{2}{a}^{\:\mathrm{2}} −\mathrm{1}\mid \\ $$$$\:\:\:\:{is}\:{differentiable}\:{on}\:\left(\:\mathrm{1},\:\mathrm{2}\:\right). \\ $$$$\:\:{find}\:{the}\:{value}\left({s}\right)\:{of}\:\:'\:\:{a}\:\:'\:. \\ $$$$\:\:........ \\ $$

Question Number 148858    Answers: 1   Comments: 0

Question Number 148856    Answers: 0   Comments: 3

pls solve

$${pls}\:{solve} \\ $$

Question Number 148854    Answers: 0   Comments: 0

∫(√((A∙B∙(√(x^2 +y^2 )))/((x^2 +y^2 )B^2 +C)))dx= ? A,B,C=const.

$$\int\sqrt{\frac{{A}\centerdot{B}\centerdot\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){B}^{\mathrm{2}} +{C}}}{dx}=\:\:? \\ $$$${A},{B},{C}={const}. \\ $$

Question Number 148849    Answers: 2   Comments: 0

lim_(x→0^+ ) ((x^3 −cos (√x) sin^2 x)/x^2 ) =?

$$\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{{x}^{\mathrm{3}} −\mathrm{cos}\:\sqrt{{x}}\:\mathrm{sin}\:^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 148848    Answers: 2   Comments: 0

lim_(x→0) ((((x+16))^(1/4) ((x+8))^(1/3) −4)/(x^2 +2x)) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{4}}]{{x}+\mathrm{16}}\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{8}}\:−\mathrm{4}}{{x}^{\mathrm{2}} +\mathrm{2}{x}}\:=?\: \\ $$

Question Number 148838    Answers: 0   Comments: 3

(1/(2×3×4)) +(1/(3×4×5))+(1/(4×5×6))+(1/(5×6×7))+(1/(6×7×8))+...+(1/(12×13×14))=?

$$\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}×\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}×\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{6}×\mathrm{7}×\mathrm{8}}+...+\frac{\mathrm{1}}{\mathrm{12}×\mathrm{13}×\mathrm{14}}=? \\ $$

Question Number 148835    Answers: 1   Comments: 0

Question Number 148825    Answers: 2   Comments: 0

Question Number 148821    Answers: 1   Comments: 0

S=(4/3)(√(m(m−m_a )(m−m_b )(m−m_c ))) m=((m_a +m_b +m_c )/2) m_a ;m_b ;m_c −mediani prove

$$\boldsymbol{{S}}=\frac{\mathrm{4}}{\mathrm{3}}\sqrt{\boldsymbol{{m}}\left(\boldsymbol{{m}}−\boldsymbol{{m}}_{\boldsymbol{{a}}} \right)\left(\boldsymbol{{m}}−\boldsymbol{{m}}_{\boldsymbol{{b}}} \right)\left(\boldsymbol{{m}}−\boldsymbol{{m}}_{\boldsymbol{{c}}} \right)} \\ $$$$\boldsymbol{{m}}=\frac{\boldsymbol{{m}}_{\boldsymbol{{a}}} +\boldsymbol{{m}}_{\boldsymbol{{b}}} +\boldsymbol{{m}}_{\boldsymbol{{c}}} }{\mathrm{2}} \\ $$$$\boldsymbol{{m}}_{\boldsymbol{{a}}} ;\boldsymbol{{m}}_{\boldsymbol{{b}}} ;\boldsymbol{{m}}_{\boldsymbol{{c}}} −\boldsymbol{{mediani}} \\ $$$$\boldsymbol{{prove}} \\ $$

Question Number 148815    Answers: 0   Comments: 0

calculate ∫_0 ^∞ (x^n /((x^(2n) +1)^2 ))dx (n≥2 integr)

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{n}} }{\left(\mathrm{x}^{\mathrm{2n}} +\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx}\:\:\:\:\:\left(\mathrm{n}\geqslant\mathrm{2}\:\:\mathrm{integr}\right) \\ $$

Question Number 148812    Answers: 1   Comments: 0

find ∫ (dx/(((√x)+(√(x+1)))((√(x−1))+(√x))))

$$\mathrm{find}\:\int\:\:\frac{\mathrm{dx}}{\left(\sqrt{\mathrm{x}}+\sqrt{\mathrm{x}+\mathrm{1}}\right)\left(\sqrt{\mathrm{x}−\mathrm{1}}+\sqrt{\mathrm{x}}\right)} \\ $$

Question Number 148809    Answers: 1   Comments: 0

Σ_(i=0) ^∞ [(−0.5x^2 )i/i!] integrate

$$\underset{\mathrm{i}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\left(−\mathrm{0}.\mathrm{5x}^{\mathrm{2}} \right)\mathrm{i}/\mathrm{i}!\right]\:\mathrm{integrate} \\ $$

Question Number 148806    Answers: 0   Comments: 1

Question Number 148804    Answers: 1   Comments: 1

Question Number 148798    Answers: 2   Comments: 0

Question Number 148797    Answers: 1   Comments: 0

Question Number 148792    Answers: 0   Comments: 0

lim_(x→0) ⌊tan^2 x⌋..evaluate the limit using squeeze theorem.

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\lfloor{tan}^{\mathrm{2}} {x}\rfloor..{evaluate}\:{the}\:{limit}\:{using}\:{squeeze} \\ $$$${theorem}. \\ $$

Question Number 149137    Answers: 0   Comments: 1

if ctg𝛂 = −2 and ((3π)/2) < α < 2π find sin𝛂 = ?

$${if}\:\:\:{ctg}\boldsymbol{\alpha}\:=\:−\mathrm{2}\:\:\:{and}\:\:\:\frac{\mathrm{3}\pi}{\mathrm{2}}\:<\:\alpha\:<\:\mathrm{2}\pi \\ $$$${find}\:\:\:{sin}\boldsymbol{\alpha}\:=\:? \\ $$

Question Number 148785    Answers: 0   Comments: 0

find the resideu f(z)=z^(−3) csc(z^2 )

$${find}\:{the}\:{resideu}\:{f}\left({z}\right)={z}^{−\mathrm{3}} {csc}\left({z}^{\mathrm{2}} \right) \\ $$

Question Number 148783    Answers: 0   Comments: 1

Question Number 148780    Answers: 2   Comments: 0

Question Number 148816    Answers: 1   Comments: 0

∫_0 ^∞ x^m e^(ix^n ) dx=??

$$\int_{\mathrm{0}} ^{\infty} {x}^{{m}} {e}^{{ix}^{{n}} } {dx}=?? \\ $$

Question Number 148776    Answers: 1   Comments: 0

Question Number 148775    Answers: 0   Comments: 0

Question Number 148894    Answers: 0   Comments: 1

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