Recently Active Calculus Questions

Let f(x) = x135 + x125 - x115 + x5 + 1. If f(x) is divided by x3 - x, then the remainder is some function of x say g(x). Find the value of g(10). ...

lim x→∞ x/ x+ x+ x ...

find the range of- [x2] - [x]2 ...

is finding areas related to the WITCH OF AGNESI curve in course for JEE?? ...

[p1.Let a function f be defined on positive integers by the setting: f(m,n)={ f(m-n,n),if m>=n; m,if m<n } COLUMN-1 COLUMN-2 A>f(32009,4)= p)2 B>f(22010,25)= q)0 c>f(52010,7)= r)3 d>f(163+173+183 +193) s)1 h ...

Find the area enclosed by: |x+y-1|+|2x+y+1|=1 ...

question by me...:P draw the graph of y=1/1+x2 very simple graph...:P ...

\lim_{n\rightarrow \propto } \frac{\left[1^{3}x \right]+\frac{1}{2}\left[2^{3}x \right]+\frac{1}{3}\left[3^{3}x \right]+......+\frac{1}{n}\left[n^{3}x \right]}{1^{2}+2^{2}+3^{2}+...+n^{2}} , where [.] denotes greatest integer ...

Q1] If ax2 -bx + 1 = 0 have 2 real roots (a,b are real) , then the greatest value of 2a-b is ? a] -1/2 (b] 0 (c] 1/2 (d] none Q2] Let the equation of a curve , x = a(θ+sinθ) ; y=a(1 - cosθ) If θ changes at a const rate k ...

Let R be the set of real numbers. Suppose f : R → R be a continuous and periodic function with period T > 0. Prove that for every a < b, \lim_{n\to \infty} \int_a^b f(nx)\ \mathrm dx = \dfrac{b-a}{T}\int_0^T f(x)\ \ma ...

If f(x) \epsilon [1,2] when x \epsilon R and for a fixedreal number p f(x+p) = 1 + f(x)- {f(x)}2 for all x \epsilon R then prove that f(x) is a peroidic function. ...

Find the following limit for \alpha >1 : \lim_{n\to \infty} n\left(\dfrac{1^\alpha + 2^\alpha + \ldots + n^\alpha}{n^{\alpha+1}}-\dfrac{1}{\alpha +1}\right) Here n is a natural number. ...

1) How to evaluate dis ?????? *Image* How to evaluate dis ?????? ...

due to lack of QOD's i had started googly from ATGS ... now that we are getting ample number of QOD's and no Graph of the day's i start this trend now :P:P Draw the graph of: y=|[x]|{x} the first graph is always easy :D ...

All of u know that Lim (Sin x)/x = 1 x→0 What will be the value of the exp if x → ∞ ...

*Image* PLEASE EXPLAIN THE APPROACH CLEARLY ...

Evaluate \int_{-1}^1\dfrac{\ln(13-6x)}{\sqrt{1-x^2}}\ \mathrm dx ...

find : \frac{29\int_{0}^{1}{\left(1-x^4 \right)^{7}}\mathrm{dx}}{4\int_{0}^{1}{\left(1-x^4 \right)^{6}}\mathrm{dx}} ...

*Image* Explain the approach,no need to solve. ...

1) show that the normal at the point (3t , 4/t ) of the curve xy = 12 cuts the curve again at the point whose parametr t1 is given by t1 = -16/9t3 ...

find all the tangents to the curve y = cos ( x+y ) ,-2pi≤x≤2pithat are parallel to the line x + 2y = 0 ...

1)) \lim_{x\rightarrow \propto } sinx/x 2) \lim_{x\rightarrow 0} \frac{\sqrt{(1-cos2x)/2}}{x} ...

Find: limn→∞Σ 1 to n: r/(4r2+1) ...

If f(x)= \sqrt{\frac{x-sinx}{x+cos^{2}x}} then find \lim_{x\rightarrow \propto } f(x) ...

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q1.) f(x).f( 1/x ) = f(x) + f 1/x ) f(3)=28 find f(4). q2.) f(x)= x4+ ax3+bx2+cx+d f(1)=10 , f(2)=20 , f(3)=30 find f(12) + f(-8) plz tell me d general way to solve such functional equations.....i hv found such questions in m ...

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The area bounded by the curve x2/3+y2/3=a2/3 Can someone please tell how to solve these kinds of questions in general? Thanks! ...

how is *Image* where *Image* i.e is how is \prod_{k=1}^{n}{\frac{1}{x^2-2x\cos \alpha+1}}=\frac{1}{n}\sum_{k=1}^{n}{\frac{1-x\cos \alpha}{x^2-2x\cos \alpha+1}} ...