For : (i) Show that by direct evaluation of an appropriate limit. (ii) Obtain the…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For f(x)=sin⁡xf(x)=\sin x: (i) Show that f′(0)=1f'(0)=1 by direct evaluation of an appropriate limit. (ii) Obtain the equation of the tangent to the curve y=sin⁡xy=\sin x at the origin. (iii) What is the angle of inclination of this tangent with the positive xx-axis?

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