30@Aditya: The answer for 1 is incorrect. For 3, we do have a unique solution. 4 has multiple correct options and b is one of them.
1. Find the largest term of the following sequence:
\text{a) } a_{n}=\frac{n^2}{n^3+200}
2. ABC is an isosceles triangle inscribed in a circle of radius r, AB=AC and h is the altitude from A to BC. If the triangle ABC has perimeter P and area Δ then find \lim_{h\rightarrow 0}512r\frac{\Delta }{p^3} .
3. If \lim_{x\rightarrow 0}\left( \cos x+a\sin bx\right)^{1/x} = e^2 , then find the value of a and b.
4. Let f(x)= ax^3+bx^2+cx+1 have extrema at x=\alpha , \beta such that \alpha\beta < 0 \text{ and } f(\alpha).f(\beta) < 0 , then the equation f(x)=0 has
a) Three equal roots
b) Three distinct real roots
c) One positive root, if f(\alpha)<0 \text{ and } f(\beta)>0
d) One negative root, if f(\alpha)>0 \text{ and } f(\beta)<0
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4 Answers
2621. just find \frac{\partial a_{n}}{\partial n}
equate it to zero. u will get n = 0, (400)1/3 .
3. i m getting ab =2 . i dont think we can get their individual values.
4. b) (think logically)
30
212)
The area is h\sqrt{2hr-h^{2}} and perimeter is 2\left(\sqrt{2hr-h^{2}}+ \sqrt{2hr} \right)
I get 512r\lim_{h\rightarrow 0}\frac{\Delta }{P^{3}} = 4
