Let t denote the greatest integer ≤t and t denote the fractional part of t. Then integral value of α for which the left hand limit of the function…

Question

Let t denote the greatest integer ≤t and t denote the fractional part of t. Then integral value of α for which the left hand limit of the function fx=1+x+(α^(2x+x)+x-1)/(2x+x) at x=0 is equal to α-4/3 is _____

MARKS Content Team · Accepted Answer

Correct answer: 3. Given, fx=1+x+(α^(2x+x)+x-1)/(2x+x) limx→0^(-)fx=α-4/3 limx→0^(-)1+x+(α^(x+x+x)+x-1)/(2x+x)=α-4/3 ⇒0+(α^(-1)-2)/(-1)=α-4/3 ⇒2-1/(α)=α-4/3 ⇒α+1/(α)=10/3 On solving above equation we get, ⇒α=3;α∈I

Let $[t]$ denote the greatest integer $\leq t$ and $\{t\}$ denote the fractional part of $t$ . Then integral value of $α$ for which the left hand limit of the function $f (x) = [1 + x] + \frac{α^{2 [x] + \{x\}} + [x] - 1}{2 [x] + \{x\}}$ at $x = 0$ is equal to $α - \frac{4}{3}$ is _____

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Relevant Questions

Let t denote the greatest integer ≤t and t denote the fractional part of t. Then integral value of α for which the left hand limit of the function fx=1+x+α2x+x+x-12x+x at x=0 is equal to α-43 is _____

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Relevant Questions

Let $[t]$ denote the greatest integer $\leq t$ and $\{t\}$ denote the fractional part of $t$ . Then integral value of $α$ for which the left hand limit of the function $f (x) = [1 + x] + \frac{α^{2 [x] + \{x\}} + [x] - 1}{2 [x] + \{x\}}$ at $x = 0$ is equal to $α - \frac{4}{3}$ is _____