The intercepts on x-axis made by tangents to thecurve, `y=int_0^x|t|dt , x in R ,`which are parallel to the line `y""=""2x`, are equalto(1) `+-2`(2) `+-3`(3) `+-4`(4) `+-1`A. `+-1`B. `+-2`C. `+-3`D. `+-4`

The intercepts on x-axis made by tangents to thecurve, `y=int_0^x|t|dt

1.	The intercepts on x-axis made by tangents to thecurve, `y=int_0^x\|t\|dt , x in R ,`which are parallel to the line `y""=""2x`, are equalto(1) `+-2`(2) `+-3`(3) `+-4`(4) `+-1`A. `+-1`B. `+-2`C. `+-3`D. `+-4`
Answer» Correct Answer - A `y=int_(0)^(x)\|t\|dt` Case I: If `xgt0` `y=int_(0)^(x)tdt=[(t^(2))/2]_(0)^(x)=(x^(2))/2implies(dy)/(dx)=x=2` (given) `implies x=2` and `y=2` `:.` eqution of tangent is `(y-2)=2(x-2)` or `y-2x+2=0` Hence `x` intercept `=` Case II: `xlt0` `-y=int_(0)^(pi)-tdt=[(-t^(2))/2]_(0)^(x)=(-x^(2))/2` `:.(dy)/(dt)=-x=2` `:. x=-2,:.y=-2`, `:.` equation iof tangent is `y+2=2(x+2)` or `2x-y+2=0` `:.x` intencept `=-1`

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`lim_(nrarroo) sum_(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))`
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