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Please solve it as soon as possible. ________________________________________________________________________________________________

```
8 months ago

Arun
25768 Points
```							Dear student image is not clear please check entry post the question with a clear image I will be happy to help you
```
8 months ago
2074 Points
```							dear student, arun is just making excuses. trust me the pic is clearly visible. he cn also download it for better visibility.coming to ur ques, such ques are best done using series expansion.f(x)= x(x^1/1! – x^3/3! + x^5/5! – …...)/2 – 1 + 1 – x^2/2! + x^4/4! – ….....= x^2/2 – x^4/12 + …... – x^2/2! + x^4/24 – …......= – x^4/12 + x^6/240 – ….. + x^4/24 – …= x^4( – 1/12+x^2/240 – …. + 1/24 – …...)hence, Lt f(x)/x^k= Lt [x^4/x^k]*( – 1/12+x^2/240 – …. + 1/24 – …...)= Lt [x^4/x^k]* Lt ( – 1/12+x^2/240 – …. + 1/24 – …...)= Lt x^(4 – k) * ( – 1/12 + 1/24)now, Lt x^(4 – k) exists finitely and non zero only when k=4. if k is less than 4, then 4 – k is greater than zero and hence lim becomes 0. if k is greater than 4, then k – 4 is greater than zero and hence lim becomes Lt 1/x^(k – 4)= ± infinityso, k=4KINDLY APPROVE :))
```
8 months ago
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• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions