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Sofiya Parihar
Subject: Maths
, asked on 7/2/18
Answer question no.12
Q.12. If
$y=x\mathrm{log}\left(\frac{x}{a+bx}\right)$
, then prove that
${x}^{3}\frac{{d}^{2}y}{d{x}^{2}}=\left(x\frac{dy}{dx}-y\right)$
.
Answer
1
Vidipta Fulpadia
Subject: Maths
, asked on 5/2/18
Q). Differentiate:
$y={\left(\mathrm{tan}x\right)}^{\mathrm{sin}x}$
Answer
2
Vidipta Fulpadia
Subject: Maths
, asked on 5/2/18
Q). Differentiate the following:
$y=\frac{1}{\sqrt{3x+7}}-\frac{1}{\sqrt{7-3x}}$
Answer
1
Somnath Sharma
Subject: Maths
, asked on 31/1/18
$Q.Iff\left(x\right)=\frac{\sqrt{2}\mathrm{cos}x-1}{\mathrm{cos}x-1},x\ne \frac{\mathrm{\pi}}{4}.Findthevalueoff\left(\frac{\mathrm{\pi}}{4}\right)sothatf\left(x\right)becomescontinuous\phantom{\rule{0ex}{0ex}}atx=\mathrm{\pi}/4.$
Answer
1
Vibhav
Subject: Maths
, asked on 30/1/18
Whats lim x->a (xloga-1)/(x-a)
Answer
1
Vibhav
Subject: Maths
, asked on 29/1/18
What are divergent and convergent limits???
Answer
1
Vibhav
Subject: Maths
, asked on 29/1/18
Whats the difference between lim h-> 0
(1) sin(1/h)/h
(2) sin(1/-h)/h
(3) sin(1/h)/-h
(4) sin(1/-h)/-h
Shouldnt also the answers be infinity as if h->0 then 1/h and 1/-h ->infinity and sin of these will be an oscillating value between -1 to 1
Also if h tends to 0, -h will also tend to 0
If the question just says lim h->0 then is it obvious that h will tend to 0 from the positive side only i.e. 0.1,0.001,0.0001 ect and NOT the negative side i.e. -0.1,-0.001,-0.0001
Answer
1
Vibhav
Subject: Maths
, asked on 29/1/18
Let f(x) = x.(e)^-2/x
If I calculate f'(0) using first principle I get teh answer as 0
However if I calculate f'(0) using product rule I dont get the same answer
Why this discrepancy in answer???
Is it because F(x) is not defined at x=0
Also can f'(c) exist if f(x) is NOT defined at x=c
Answer
1
Vibhav
Subject: Maths
, asked on 29/1/18
Whats lim h->0 sin(1/h)/h please give the relevant reason as well
Answer
1
Vibhav
Subject: Maths
, asked on 29/1/18
Please solve Q8
Answer
2
Abhishek
Subject: Maths
, asked on 28/1/18
Solve the limits??
Q.
$\underset{x\to 0}{\mathrm{lim}}\left[\frac{100\mathrm{sin}x}{x}\right]+\left[\frac{100\mathrm{tan}x}{x}\right]$
Answer
1
Abhishek
Subject: Maths
, asked on 28/1/18
$Q.\underset{x\to 0}{\mathrm{lim}}\frac{x\sqrt{{y}^{2}-(x-y{)}^{2}}}{(\sqrt{8xy-y{x}^{2}}+\sqrt{8xy}{)}^{3}}$
Answer
1
Jassimrat Kaur
Subject: Maths
, asked on 28/1/18
Please solve example 43
Answer
1
Vibhav
Subject: Maths
, asked on 28/1/18
In this solution isnt (-h)^(1/2) an imaginary number???
Also how is sin(1/h) as h->0 = h as h->0???
Lim h ->0 (sinh/h) = 1 is applicable on if h tends to 0
But if h->0 (1/h) tends to infinity so this rule isnt applicable
Also in this question 0Then (-h)^(1/3) is a real number
Isnt this question a liitle incomplete???
Answer
1
Vibhav
Subject: Maths
, asked on 28/1/18
Whats the difference between
(1) lim h->0 sin(1/h)
(2) lim h->0 sin(-1/h)
Arent both these one and the same thing???
Answer
1
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Q.12. If $y=x\mathrm{log}\left(\frac{x}{a+bx}\right)$, then prove that ${x}^{3}\frac{{d}^{2}y}{d{x}^{2}}=\left(x\frac{dy}{dx}-y\right)$.

$y={\left(\mathrm{tan}x\right)}^{\mathrm{sin}x}$

$y=\frac{1}{\sqrt{3x+7}}-\frac{1}{\sqrt{7-3x}}$

(1) sin(1/h)/h

(2) sin(1/-h)/h

(3) sin(1/h)/-h

(4) sin(1/-h)/-h

Shouldnt also the answers be infinity as if h->0 then 1/h and 1/-h ->infinity and sin of these will be an oscillating value between -1 to 1

Also if h tends to 0, -h will also tend to 0

If the question just says lim h->0 then is it obvious that h will tend to 0 from the positive side only i.e. 0.1,0.001,0.0001 ect and NOT the negative side i.e. -0.1,-0.001,-0.0001

If I calculate f'(0) using first principle I get teh answer as 0

However if I calculate f'(0) using product rule I dont get the same answer

Why this discrepancy in answer???

Is it because F(x) is not defined at x=0

Also can f'(c) exist if f(x) is NOT defined at x=c

Q. $\underset{x\to 0}{\mathrm{lim}}\left[\frac{100\mathrm{sin}x}{x}\right]+\left[\frac{100\mathrm{tan}x}{x}\right]$

Also how is sin(1/h) as h->0 = h as h->0???

Lim h ->0 (sinh/h) = 1 is applicable on if h tends to 0

But if h->0 (1/h) tends to infinity so this rule isnt applicable

Also in this question 0Then (-h)^(1/3) is a real number

Isnt this question a liitle incomplete???

(1) lim h->0 sin(1/h)

(2) lim h->0 sin(-1/h)

Arent both these one and the same thing???