limits
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find n such \ that \lim_{x\to 0}\frac{\cos^2{x}-\cos{x}-e^x\cdot\cos{x} + e^x - \frac{x^3}{2}}{x^n} \ \ is finite
find n such \ that \lim_{x\to 0}\frac{\cos^2{x}-\cos{x}-e^x\cdot\cos{x} + e^x - \frac{x^3}{2}}{x^n} \ \ is finite
12 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.Ansh Agarwal
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It shall be maximum positive value of n imo
The answer is 4
n is a natural number is given
@Ansh Agarwal did you try taylor series
To no avail, didn't give the answer.
Taylor would work i guess? Numerator tends to
$(1-\frac{x^{2}}{2})^{2}-(1-\frac{x^{2}}{2})(1+x+\frac{x^{2}}{2})+(1+x+\frac{x^{2}}{2})-\frac{x^{3}}{2}-(1-\frac{x^{2}}{2})$
SirLancelotDuLac
This comes out to be \frac{x^{4}}{2} so min. value of n is 4 and value of limit at that is 1/2.
Further L' Hopitals works out as well.
Thanks, it worked , probably made a mistake or something the first time
+solved @SirLancelotDuLac @Optimus43
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