What is the limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h ?

The limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h is 1/2

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limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h

h \to 0 lim (\frac{sin ( \frac{π}{3} + h ) - sin ( \frac{π}{3} )}{h})

\frac{1}{2}

Decimal

0.5

Solution steps

h \to 0 lim (\frac{sin ( \frac{π}{3} + h ) - sin ( \frac{π}{3} )}{h})

Apply L'Hopital's Rule

= h \to 0 lim (\frac{cos ( h + \frac{π}{3} )}{1})

Plug in the value

h = 0

= \frac{cos ( 0 + \frac{π}{3} )}{1}

Simplify

\frac{cos ( 0 + \frac{π}{3} )}{1} : \frac{1}{2}

= \frac{1}{2}

y^{^{''}} + y = cos^{2} (t), y (0) = 0, y^{^{'}} (0) = 0

\int e^{c o s (2 x)} sin (x) cos (x) d x

(t^{2} + x^{2}) d t + (2 t x - x) d x = 0

x \to 0 - lim (- 7 x^{2} + 5 x)

d er i v a t i v e y = \frac{6 x - 1}{8 x + 3}

What is the limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h ?
The limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h is 1/2