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15 votes
5 answers
451
GATE CSE 1987 | Question: 1-xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ hasAll complex rootsAt least one real rootFour pairs of imaginary rootsNone of the above
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1 votes
2 answers
452
Targate
How to solve this?
How to solve this?
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0 votes
0 answers
454
GATE [Math]
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2 votes
2 answers
456
GATE [Math]
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0 votes
1 answer
457
math calculus
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4 votes
1 answer
458
Virtual Gate Test Series: Calculus - Integration
Let $\frac{d}{dx} [f(x)] = \frac{e^{sinx}}{x} , x > 0 .$ If $\int_{1}^{4}(\frac{2e^{sinx^{2}}}{x}) dx = f(k) - f(1)$ where limits of integration is from $1$ to $4$ , then $k =?$
Let $\frac{d}{dx} [f(x)] = \frac{e^{sinx}}{x} , x 0 .$If $\int_{1}^{4}(\frac{2e^{sinx^{2}}}{x}) dx = f(k) - f(1)$ where limits of integration is from $1$ to $4$ , then $...
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1 votes
3 answers
459
Evaluate the following definite integral ?
Evaluate the following definite integral : $\int \limits_0^1 \log \left(\frac{1}{x} - 1 \right)$
Evaluate the following definite integral :$\int \limits_0^1 \log \left(\frac{1}{x} - 1 \right)$
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1 votes
1 answer
460
Continuity
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3 votes
2 answers
461
limits
what is the value of $\textstyle \lim_{x \to 2}\frac{x-2}{\log(x-1)}$
what is the value of$\textstyle \lim_{x \to 2}\frac{x-2}{\log(x-1)}$
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2 votes
2 answers
462
Gate 2014 CE Set 2
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
The expression $\lim_{a \to 0}\frac{x^{a}-1}{a}$ is equal to (A)$\log x$ (B)0 (c)$x\log x$ (D)$\infty$
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3 votes
2 answers
464
Calculus
Can anyone tell me range of f(x)=|sinx|+|cosx|
Can anyone tell me range of f(x)=|sinx|+|cosx|
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0 votes
1 answer
465
limits
$\lim_{x \to 0}x\log _x a$ $(A)0$ $(B)\log_ae$ $(C)1$ $(D)\log a$
$\lim_{x \to 0}x\log _x a$$(A)0$ $(B)\log_ae$$(C)1$ ...
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10 votes
1 answer
466
ISRO2016-3
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by $0$ $-1$ $1$ $\frac{1}{2}$
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by$0$$-1$$1$$\frac{1}{2}$
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0 votes
1 answer
467
What is the difficulty level of Calculus questions?
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
I find Calculus part very difficult, what is the difficulty level of Calculus? also please let me know which part should I focus in Mathematic.
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0 votes
3 answers
468
Limit
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
Can we calculate. $\textstyle \lim_{n \to \infty}\frac{2^{n}}{3^{n}}$ if yes then what is the value.
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5 votes
1 answer
469
ISRO2011-59
$n$-th derivative of $x^n$ is $nx^{n-1}$ $n^n.n!$ $nx^n!$ $n!$
$n$-th derivative of $x^n$ is$nx^{n-1}$$n^n.n!$$nx^n!$$n!$
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0 votes
0 answers
470
calculus differentiation question
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0 votes
0 answers
471
Calculus
​​If $a=\Sigma_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}, \: b=\Sigma_{n=1}^{\infty} \frac{x^{3n-2}}{(3n-2)!} $ and $c=\Sigma_{n=1}^{\infty} \frac{x^{3n-1}}{(3n-1)!} $, then the value of $(a^3+b^3+c^3-3abc)$ is 1 0 -1 -2
​​If $a=\Sigma_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}, \: b=\Sigma_{n=1}^{\infty} \frac{x^{3n-2}}{(3n-2)!} $ and $c=\Sigma_{n=1}^{\infty} \frac{x^{3n-1}}{(3n-1)!} $, the...
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2 votes
1 answer
472
calculus
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to (a) $0$ (b) $-1/2$ (c) $1/2$ (d) None of the above
$\lim_{x \to \infty}\left (\frac{1}{1-x^{2}} + \frac{2}{1-x^{2}}+\dots+\frac{x}{1-x^{2}}\right )$ is equal to(a) $0$(b) $-1/2$(c) $1/2$(d) None of the above
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6 votes
1 answer
473
ISRO2009-50
The value of $x$ at which $y$ is minimum for $y=x^2 -3x +1 $ is $-3/2$ $3/2$ $0$ $-5/4$
The value of $x$ at which $y$ is minimum for $y=x^2 -3x +1 $ is$-3/2$$3/2$$0$$-5/4$
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5 votes
1 answer
474
ISRO2009-49
$x=a \cos(t), y=b \sin(t)$ is the parametric form of Ellipse Hyperbola Circle Parabola
$x=a \cos(t), y=b \sin(t)$ is the parametric form ofEllipseHyperbolaCircleParabola
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0 votes
1 answer
475
maxima minima
maxima minima of 2^(sinx)/2^(cosx)
maxima minima of 2^(sinx)/2^(cosx)
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3 votes
2 answers
477
Lagrange 's Mean Value Theorem 2
If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___
If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___
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0 votes
1 answer
478
Lagrange 's Mean Value Theorem
Question: The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______ My Attempt : STEP 1: $f(x)$ is polynomial function therefore continuous STEP 2: $f(x)$ is ... How to proceed further?
Question:The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______My Attempt :STEP 1: $f(x)...
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26 votes
4 answers
480
GATE CSE 2016 Set 1 | Question: 3
$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_\_\_\_$
$$\lim _{x\rightarrow 4}\frac{\sin(x-4)}{x-4}=\_\_\_\_\_\_\_\_\_\_\_\_$$
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