Use the definition of derivative to find the derivative of f(x) = sin(7x) Evaluate the following limits, if they exist. (Do not use L'Hospital's rule) lim h→1 (sqrt(h^2 + 15) - sqrt(h + 15)) / (sqrt(h + 3) - 2)
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Step 1
Given f(x) = sin(7x), we have f'(x) = lim(h->0) [sin(7(x+h)) - sin(7x)] / h Using the trigonometric identity sin(A+B) - sin(A) = 2cos((A+B)/2)sin((A-B)/2), we get: f'(x) = lim(h->0) [2cos(7(x+h) + 7x)/2 * sin(7(x+h) - 7x)/2] / h f'(x) = lim(h->0) [2cos(7x + 7h)/2 Show more…
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