InterviewSolution
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InterviewSolution
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`lim_(x rarr pi/4)(tan^3x-tanx)/(cos(x+pi/4)` |
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Answer» Correct Answer - `-4` Given limit `=lim_(xto(pi)/(4))(tanx(tanx+1)(sinx-cosx))/(cosx.cos(x+(pi)/(4)))` `=lim_(xto(pi)/(4))(tanx(tanx+1)(sinx-cosx))/(cosx.cos(x+(pi)/(4)))` `=-lim_(xto(pi)/(4))(tanx(tanx+1)(cosx-sinx))/(cosx. cos(x+(pi)/(4)))` `=-sqrt2lim_(xto(pi)/(4))(tanx(tanx+1)((1)/(sqrt2)cosx-(1)/(sqrt2)sinx))/(cosx.cos(x+(pi)/(4)))` `=-sqrt2lim_(xto(pi)/(4))(tanx(tanx+1).cos(x+(pi)/(4)))/(cosx. cos(x+(pi)/(4)))=-sqrt2lim_(xto(pi)/(4))(tanx(tanx+1))/(cosx)` `=-sqrt2.(1xx(1+1))/(((1)/(sqrt2)))=-4.` |
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