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Question Number 95644 Answers: 0 Comments: 0

If f is derivable at x_0 , show that lim_(x→x_0 ) f(x)=f(x_0 )

$$\mathrm{If}\:\mathrm{f}\:\mathrm{is}\:\mathrm{derivable}\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} ,\:\mathrm{show}\:\mathrm{that}\:\underset{\mathrm{x}\rightarrow\mathrm{x}_{\mathrm{0}} } {\mathrm{lim}f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}_{\mathrm{0}} \right) \\ $$

Question Number 95643 Answers: 1 Comments: 0

Show that the function f(x)=x^3 is derivable at all points x_0 ∈R and that f′(x_0 )=3x_0 ^2

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:\mathrm{is}\:\mathrm{derivable}\:\mathrm{at}\:\mathrm{all} \\ $$$$\mathrm{points}\:\mathrm{x}_{\mathrm{0}} \in\mathbb{R}\:\mathrm{and}\:\mathrm{that}\:\mathrm{f}'\left(\mathrm{x}_{\mathrm{0}} \right)=\mathrm{3x}_{\mathrm{0}} ^{\mathrm{2}} \\ $$

Question Number 95639 Answers: 1 Comments: 1

find the equation of the circle containing the point (−2,2) and passing throught the points of intersection of the two circle x^2 +y^2 +3x−2y−4=0 and x^2 +y^2 −2x−y−6=0

$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\: \\ $$$$\mathrm{containing}\:\mathrm{the}\:\mathrm{point}\:\left(−\mathrm{2},\mathrm{2}\right)\:\mathrm{and} \\ $$$$\mathrm{passing}\:\mathrm{throught}\:\mathrm{the}\:\mathrm{points}\:\mathrm{of}\: \\ $$$$\mathrm{intersection}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{circle}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{3x}−\mathrm{2y}−\mathrm{4}=\mathrm{0}\:\mathrm{and}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{2x}−\mathrm{y}−\mathrm{6}=\mathrm{0} \\ $$

Question Number 95638 Answers: 1 Comments: 0

a\Show that f(x)=(√x) is derivable at all points x_0 >0 and that f′(x_0 )=(1/(2x_0 )) b\ Show that the function f(x)=(√x) (continuous at x_0 =0) is not derivable at x_0 =0

$$\mathrm{a}\backslash\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}}\:\mathrm{is}\:\mathrm{derivable}\:\mathrm{at}\:\mathrm{all}\:\mathrm{points}\:\mathrm{x}_{\mathrm{0}} >\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{that}\:\mathrm{f}'\left(\mathrm{x}_{\mathrm{0}} \right)=\frac{\mathrm{1}}{\mathrm{2x}_{\mathrm{0}} } \\ $$$$\mathrm{b}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{x}}\:\left(\mathrm{continuous}\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{0}\right) \\ $$$$\mathrm{is}\:\mathrm{not}\:\mathrm{derivable}\:\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{0} \\ $$

Question Number 95636 Answers: 2 Comments: 0

Find the equation of the tangent(T_0 ) to y=x^3 −x^2 −x at x_0 =2. Find x_1 such that the tangent T_1 at x_1 be parallel to T_0 .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangent}\left(\mathrm{T}_{\mathrm{0}} \right)\:\mathrm{to}\:\mathrm{y}=\mathrm{x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} −\mathrm{x} \\ $$$$\mathrm{at}\:\mathrm{x}_{\mathrm{0}} =\mathrm{2}.\:\mathrm{Find}\:\mathrm{x}_{\mathrm{1}} \:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{T}_{\mathrm{1}} \:\mathrm{at}\:\mathrm{x}_{\mathrm{1}} \\ $$$$\mathrm{be}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{T}_{\mathrm{0}} . \\ $$

Question Number 95635 Answers: 1 Comments: 0

Show that if a function is even and derivable then f′(x) is an odd function.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{a}\:\mathrm{function}\:\mathrm{is}\:\mathrm{even}\:\mathrm{and}\:\mathrm{derivable}\:\mathrm{then} \\ $$$$\mathrm{f}'\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function}. \\ $$

Question Number 95634 Answers: 1 Comments: 0

solve ∣x+(1/x)∣ > 2

$$\mathrm{solve}\:\mid{x}+\frac{\mathrm{1}}{{x}}\mid\:>\:\mathrm{2}\: \\ $$

Question Number 95624 Answers: 1 Comments: 0

∫_1 ^5 x(∫f(x)dx) dx = 24 ∫_1 ^3 (2−f(x))dx ?

$$\overset{\mathrm{5}} {\int}_{\mathrm{1}} {x}\left(\int\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right)\:{dx}\:=\:\mathrm{24} \\ $$$$\overset{\mathrm{3}} {\int}_{\mathrm{1}} \left(\mathrm{2}−\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}\:?\: \\ $$

Question Number 95608 Answers: 3 Comments: 2

Question Number 95604 Answers: 1 Comments: 3

Question Number 95601 Answers: 0 Comments: 1

1z 1

$$\mathrm{1}{z} \\ $$$$ \\ $$$$\mathrm{1} \\ $$

Question Number 95600 Answers: 1 Comments: 0

solve the differential equation L(d^2 q/dt^2 )+R(dq/dt)+(1/C)q=εcosωt which is in R.L.C circuit with forced oscillation where L is inductance R is resistance C is capacitanace q is charge ε is motion emf t is time

$${solve}\:{the}\:{differential}\:{equation} \\ $$$${L}\frac{{d}^{\mathrm{2}} {q}}{{dt}^{\mathrm{2}} }+{R}\frac{{dq}}{{dt}}+\frac{\mathrm{1}}{{C}}{q}=\varepsilon{cos}\omega{t} \\ $$$${which}\:{is}\:{in}\:{R}.{L}.{C}\:{circuit}\:{with}\:{forced}\:{oscillation} \\ $$$${where}\:{L}\:{is}\:{inductance} \\ $$$${R}\:{is}\:{resistance} \\ $$$${C}\:{is}\:{capacitanace} \\ $$$${q}\:{is}\:{charge} \\ $$$$\varepsilon\:{is}\:{motion}\:{emf} \\ $$$${t}\:{is}\:{time} \\ $$

Question Number 95598 Answers: 0 Comments: 0

If sin^(−1) x_1 +sin^(−1) x_2 +...+sin^(−1) x_(2n) =nπ, then Σ^(2n) _(i, j=1_(i ≠ j) ) x_i x_j =

$$\mathrm{If}\:\:\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}} +...+\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:\:\underset{\underset{{i}\:\neq\:{j}} {{i},\:{j}=\mathrm{1}}} {\overset{\mathrm{2}{n}} {\sum}}\:\:\:{x}_{{i}} \:{x}_{{j}} \:= \\ $$

Question Number 95597 Answers: 0 Comments: 1

The value of cosec^2 (π/7)+cosec^2 ((2π)/7)+cosec^2 ((3π)/7) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cosec}^{\mathrm{2}} \:\frac{\pi}{\mathrm{7}}+\mathrm{cosec}^{\mathrm{2}} \:\frac{\mathrm{2}\pi}{\mathrm{7}}+\mathrm{cosec}^{\mathrm{2}} \:\frac{\mathrm{3}\pi}{\mathrm{7}}\:\mathrm{is} \\ $$

Question Number 95593 Answers: 0 Comments: 2

if f(x) = ((sin x)/((1 + x^2 +x^6 )^2 )) is odd, find ∫_(−3) ^3 f(x) dx

$$\mathrm{if}\:{f}\left({x}\right)\:=\:\frac{\mathrm{sin}\:{x}}{\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \:+{x}^{\mathrm{6}} \right)^{\mathrm{2}} }\:\mathrm{is}\:\mathrm{odd}, \\ $$$$\mathrm{find}\:\underset{−\mathrm{3}} {\overset{\mathrm{3}} {\int}}{f}\left({x}\right)\:{dx} \\ $$

Question Number 95586 Answers: 1 Comments: 1

find ∫ (dx/(x^n (x+1)^m )) m and n integr