Shrink the numerator

Calculus Level 4

f ( x ) = A sin ⁡ ( x ) + B sin ⁡ ( 2 x ) + sin ⁡ ( 3 x ) x 5 \large f(x) = \frac{ A \sin(x) + B \sin(2x) + \sin(3x) }{x^5}

For x ≠ 0 x \ne 0 , let f ( x ) f(x) be expressed as above for constants A , B A,B .

If f ( x ) f(x) is continuous at x = 0 x=0 , find A + B A+B .


The answer is 1.

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Rohit Ner by Rohit Ner , 22, India

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1 solution

Apply L'Hospital till in the denomiator you get x x .

Note:

L'Hospital can be used only when the limit attains 0 0 \dfrac{0}{0} . Find suitable conditions in A and B.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Can you elaborate on it? Your solution barely mentions any key points. Furthermore, you don't actually need to apply L'Hopital Rule. Hint: Maclaurin series.

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