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Consider f(x)=int_(-1)^(x)(e^((x-t)/(x-2-t))dt)/(x-2-t)^(2) Q. The y-intercept of tangent drawn to graph of y=f(x) at x=-1 is |
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Answer» Solution :Put `(1)/(X-2-t)=U` `implies(1)/((x-2-t)^(2))dt=du` `f(x)=int_((1)/(x-1))^(-(1)/(2))e.e^(2u)du` `f(x)=(e)/(2).(e^(-1)-e^((2)/(x-1)))` `f(x)=(1)/(2)-(e)/(2).e^((2)/(x-1))` (1) `f(x)lt(1)/(2)` for all `xepsilonR` `implies` Greatest INTEGER in the Range `=0` (2) `f^(')(x)=(e)/((x-1)^(2))e^((2)/(x-1))` `f^(')(-1)=(1)/(4)(x+1)` `impliesy` intercept`=(1)/(4)` |
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