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प्रश्न
Find the value of 'k' if the function
f(x) = `(tan 7x)/(2x)`, for x ≠ 0.
= k for x = 0.
is continuous at x = 0.
योग
उत्तर
Given :
f(x) = `(tan 7x)/(2x)`, for x ≠ 0.
= k for x = 0.
∴ f(0) = k
Now, `lim_( x -> 0) f(x) = lim_( x -> 0) (tan 7x)/(2x)`
= `lim_( x -> 0) (tan 7x)/(7x)(7/2)`
= `1 xx 7/2`
= `7/2`
As function f(x) is continuous at x = 0
∴ `lim_(x -> 0) f(x) = f(0) = k`
k = `7/2`
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