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Q no. of solutions e^x= lnx Q graph of [4sinx] [.]greatest integer and how to find pts of discontinuity using the graph ???

Tushar Makkar
37 Points
10 years ago

Q2; we can find the points of discontinuity by plotting graph of [4sinx]... this can be done by drawing horizontal line parallel to x axis and terminating it whenever [4sinx ] becomes integer ...

2nd method : just find the no. of points where 4 sinx becomes integer because [] graph is discontinuous at integers so ans is like sin^(-1) 4,.... and so on...

Q1: plot both graphs and find there intersection points  there is no solution because of foll:

we devide it into intervals

1st: frm (- infinity) to 1: e^x graph is above x axis while lnx graph is below x axis so no solution

2nd:frm 1 to infinity : the slope of e^x is e^x while that of lnx is 1/x( we can findit by differentiating the curves) and at 1 the slope of e^x is e which is nearly 2.7 while that of lnx is 1 and the slope of e^x is continuously increasing while that of lnx is decreasing so...lnx will never be able to catch up e^x and hence no intersection and hence no solution

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear student,

Draw both the graphs and where there is sharp turn that is the point of discontinuity...

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