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Question Number 25974 Answers: 0 Comments: 0

A cowbell coffee at 85°C is placed in a freezer at 0°C.The temperature of the coffee decreases exponentially;so that after 5 minutes it is 30°C. i.)What is the temperature after 3minute? ii)how long will it take for the temperature to drop to 5°C?

$A c o w b e l l c o f f e e a t 85 ° C i s p l a c e d i n a$ $f r e e z e r a t 0 ° C . T h e t e m p e r a t u r e o f t h e$ $c o f f e e d e c r e a s e s e x p o n e n t i a l l y; s o t h a t$ $a f t e r 5 m i n u t e s i t i s 30 ° C .$ $i .) W h a t i s t h e t e m p e r a t u r e a f t e r 3 m i n u t e ?$ $i i) h o w l o n g w i l l i t t a k e f o r t h e t e m p e r a t u r e$ $t o d r o p t o 5 ° C ?$

Question Number 25973 Answers: 1 Comments: 0

((k.2^k +2.2^k +2k+4)/2)=(k+3)2^k

$\frac{k . 2^{k} + 2 . 2^{k} + 2 k + 4}{2} = (k + 3) 2^{k}$

Question Number 25969 Answers: 0 Comments: 1

C_0 +2C_1 +3C_2 +..........+(n+1)C_n =(n+2)2^(n−1) using Bionomial teorm

$C_{0} + {2 C}_{1} + {3 C}_{2} + . . . . . . . . . . + (n + 1) C_{n} = (n + 2) 2^{n - 1}$ $using Bionomial teorm$

Question Number 26016 Answers: 0 Comments: 0

Question Number 26013 Answers: 1 Comments: 0

Question Number 25949 Answers: 0 Comments: 0

Question Number 25943 Answers: 1 Comments: 0

Question Number 26096 Answers: 0 Comments: 0

Question Number 25940 Answers: 0 Comments: 0

every extreme point is a critical point but every critical is not a extreme point justify it

$e v e r y e x t r e m e p o i n t i s a c r i t i c a l$ $p o i n t b u t e v e r y c r i t i c a l i s n o t a$ $e x t r e m e p o i n t j u s t i f y i t$

Question Number 25934 Answers: 1 Comments: 2

Question Number 25899 Answers: 1 Comments: 1

8a^6 +5a^3 +1=factorize

$8 a^{6} + 5 a^{3} + 1 = f a c t o r i z e$

Question Number 25894 Answers: 0 Comments: 1

Question Number 25846 Answers: 0 Comments: 3

determine the interval on which the given function is continuous f(x)= { ((sin (1/x)),(x≠0)),(x,(x=0)) :}

$d e t e r m i n e t h e i n t e r v a l o n w h i c h t h e$ $g i v e n f u n c t i o n i s c o n t i n u o u s$ $f (x) = {\begin{cases} \sin \frac{1}{x} & x \neq 0 \\ x & x = 0 \end{cases}$

Question Number 25838 Answers: 0 Comments: 4

Question Number 25854 Answers: 1 Comments: 0

find (dy/dx) for y=(√(x+(√(x+(√(x+(√(x.........))))))))

$f i n d \frac{d y}{d x} f o r y = \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x . . . . . . . . .}}}}$

Question Number 25828 Answers: 2 Comments: 1

Two particles A and B of equal masses m are tied with an inextensible string of length 2l. The initial distance between A and B is l. Particle A is given speed v. Find the speed of particle A and B just after the string becomes taut.

$T w o p a r t i c l e s A a n d B o f e q u a l m a s s e s$ $m a r e t i e d w i t h a n i n e x t e n s i b l e s t r i n g$ $o f l e n g t h 2 l . T h e i n i t i a l d i s t a n c e$ $b e t w e e n A a n d B i s l . P a r t i c l e A i s$ $g i v e n s p e e d v . F i n d t h e s p e e d o f$ $p a r t i c l e A a n d B j u s t a f t e r t h e s t r i n g$ $b e c o m e s t a u t .$

Question Number 25825 Answers: 1 Comments: 0

f:R→R is defined by f(x)={1_(−1 if x∉Z) if x∈Z Is f continuous at x=1 and x=−(3/2) ∫?

$f : R \to R i s d e f i n e d b y$ $f (x) = {\underset{- 1 i f x \notin Z}{1} if x \in Z$ $I s f c o n t i n u o u s a t x = 1 a n d x = - \frac{3}{2} \int ?$

Question Number 25814 Answers: 1 Comments: 0

find δ>0 such that ∣f(x)+1∣<0.01 when 0<∣x−2∣<δ,where f(x)=((x^2 −5x+6)/(x−2)),hence use ε_δ definition to show that ((lim)/(xtends 2))f(x)=−1

$f i n d δ > 0 s u c h t h a t ∣ f (x) + 1 ∣< 0.01$ $w h e n 0 <∣ x - 2 ∣< δ, w h e r e$ $f (x) = \frac{x^{2} - 5 x + 6}{x - 2}, h e n c e u s e ε_δ$ $d e f i n i t i o n t o s h o w t h a t$ $\frac{l i m}{x t e n d s 2} f (x) = - 1$

Question Number 25800 Answers: 2 Comments: 0

is sum of two periodic function is also periodic give reason

$i s s u m o f t w o p e r i o d i c f u n c t i o n i s$ $a l s o p e r i o d i c g i v e r e a s o n$

Question Number 25778 Answers: 1 Comments: 0

Question Number 25745 Answers: 1 Comments: 0

find the volume of the solid generated by thr revolution of the curve y(x^2 +a^2 )=a^3 about itd asymptote.

$f i n d t h e v o l u m e o f t h e s o l i d$ $g e n e r a t e d b y t h r r e v o l u t i o n o f t h e$ $c u r v e y (x^{2} + a^{2}) = a^{3} a b o u t i t d$ $a s y m p t o t e .$

Question Number 25744 Answers: 1 Comments: 0

find the surface area of the solid formed by the rotation of the arc of the cycloid x=a(t+sin t), y=a(1+cost) about x axis

$f i n d t h e s u r f a c e a r e a o f t h e s o l i d$ $f o r m e d b y t h e r o t a t i o n o f t h e a r c o f$ $t h e c y c l o i d x = a (t + s i n t),$ $y = a (1 + c o s t) a b o u t x a x i s$

Question Number 25656 Answers: 0 Comments: 3

trace the curve y^2 (x+1)=x^2 (3−x) clearly stating all the properties used for tracing.

$t r a c e t h e c u r v e$ $y^{2} (x + 1) = x^{2} (3 - x)$ $c l e a r l y s t a t i n g a l l t h e p r o p e r t i e s u s e d$ $f o r t r a c i n g .$

Question Number 25655 Answers: 0 Comments: 0

use lagranges mean value theorem to prove that x<sin^(−1) x<(x/(√(1−x^2 ))),0<x<1.

$u s e l a g r a n g e s m e a n v a l u e t h e o r e m t o$ $p r o v e t h a t$ $x < {s i n}^{- 1} x < \frac{x}{\sqrt{1 - x^{2}}}, 0 < x < 1 .$

Question Number 25635 Answers: 0 Comments: 1

let f be the function defined on [−1,1] by f(x)={ { ((−1,if x is rational)),((1,if x is irrational.)) :} find U(P,f) and L(P,f).f is integrable or not ?

$l e t f b e t h e f u n c t i o n d e f i n e d o n$ $[- 1, 1] b y$ $f (x) = {{\begin{cases} - 1, i f x i s r a t i o n a l \\ 1, i f x i s i r r a t i o n a l . \end{cases}$ $f i n d U (P, f) a n d L (P, f) . f i s i n t e g r a b l e$ $o r n o t ?$

Question Number 25634 Answers: 1 Comments: 0

find the equation of the tangent to the curve (√x)+(√y)=(√a) at any point (x,y)on it.

$f i n d t h e e q u a t i o n o f t h e t a n g e n t t o$ $t h e c u r v e \sqrt{x} + \sqrt{y} = \sqrt{a} a t a n y p o i n t$ $(x, y) o n i t .$

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