If `0ltx<1,` then="" prove="" that="" `(1-2x)="" (1-x="x^2)+(2x-4x^3)/(1-x^2+x^4)+(4x^3-8x^7)/(1-x^4+x^8)+....oo=(1+2x)/(1+x+x^2)`

Find the value of 3/2x^2+5/3x^3+7/4x^4 +. . . +oo if 0 ltx lt 1

Given : f(x)={(1/(x^2)","1ltxltoo,),(0",",elsewhere):} is p.d.f. of c.r.v X If A:1 lt x lt2 and B:4ltx lt5 , then : P (A cupB)=…

If : f(x) {:(=1", ... "0 ltx le (3pi)/4), (= 2 .sin ((2x)/9) ", ..." (3pi)/4lt x lt pi):} then :

Let f(x) = {{:({1+|sin x|}^(a//|sin x|)", " pi/6 lt x lt 0),(" b, " x = 0 ),(e^(tan 2x//tan 3x) ", "0ltx ltpi/6):} Determine a and b such that f(x) is continous at x = 0.

The intervals of the set {x:x in R and -3 ltx le 15} is

In the given figure, PS = SQ = SR and ltSPQ = 54^(@) . Find the measure of ltx .

Which one of the following is correct ? If 4 ltx^(2) le9 , then

(sin^-1x)^2-(cos^-1x)^2=a for o ltx lt1 find 2x^2-1

Discuss the continous of the following function on its domain, where f(x)=x^(2)-4, "for" 0lex le2 =2x+3, "for" 2 ltx le4 =x^(2)-05, "for" 4 lt x le6.

If the function f(x)= {(5", " x le 2),(ax+b", "2 ltx le 10 ),(21", " x gt 10 ):} continuous ,find the values of a and b