Limits
Parameter limit by expansion
nta_pyq_2025_apr
Grade 12
Question:
For$\alpha$,$\beta$,$\gamma$,$\ in $R, if lim x 2 sin$\alphax$+($\gamma$-1)e$x = 3$, then$\beta$+$\gamma$-$\alpha$is equal to: x$\to$0 sin 2x-$\betax$
Step-by-Step Solution
Key Concept: Expand the expression near the limiting point using the appropriate standard trigonometric, logarithmic, or exponential approximation.
2 2 x x ($\alphax$) + ($\gamma$- 1)$(1 + )$1 (1) lim x$\to$10 8x$3 = 3$2x - -$\betax$6 2 3 ($\gamma$- 1) + ($\gamma$- 1)x +$\alphax$$lim = 3$4 x$\to$0 3 (2 -$\beta$)$x - x$3 -3$\alpha$$\gamma$- 1,$\beta$= 2, = +3 $\Rightarrow$$\alpha$= -4 4$\beta$+$\gamma$-$\alpha$= 7
Correct Answer: 1