lim 3x​3+4x2-7/2x2+5x-7
​x->1

Dear Student,

limx13x3 + 4x2 - 72x2 + 5x - 7Let px = 3x3 + 4x2 - 7Put x = 1 in px, we getp1 = 313 + 412 - 7 = 3 + 4 - 7 = 0 So, x-1 is a factor of px.Now, we will divide px by x-1.


So, px = 3x3 + 4x2 - 7=x - 13x2 + 7x + 7Let gx = 2x2 + 5x - 7=2x2 + 7x - 2x - 7=x2x + 7 - 12x + 7=x - 12x + 7Now,      limx1  3x3 + 4x2 - 7 2x2 + 5x - 7=limx1x - 13x2 + 7x + 7x - 12x + 7=limx13x2 + 7x + 72x + 7=3×12 + 7 × 1 + 72×1 + 7=3 + 7 + 72 + 7=179

Regards

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Hi Aishwarya, as x --> 1 we get 0/0 which is indeterminate
So we can apply l'Hopithal Rule. So we can differentiate numerator and denominator separately
So we have 9 x^2 + 8 x / 4 x + 5
Now as x --> 1 then we get 9+8/4+5 =17/9
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