Suppose that the velocity \( v(t) \) (in meters per second) of a sky diver falling near the Earth's surface is given by the following exponential function, where time \( t \) is the time after diving measured in seconds. \[ v(t)=74-74 e^{-0.19 t} \] How many seconds after diving will the sky diver's velocity be 61 meters per second? Round your answer to the nearest tenth, and do not round any intermediate computations. seconds

11. Find the values of \( a \) and \( b \) that make \( f \) continuous everywhere. \[ f(x)=\left\{\begin{array}{ll}\frac{x^{2}-4}{x-2} & \text { if } x<2 \\ a x^{2}-b x+3 & \text { if } 2 \leq x<3 \\ 2 x-a+b & \text { if } x \geq 3\end{array}\right. \]

\( \lim _ { x \rightarrow 0 } \frac { 3 ( x - \operatorname { cts } x ) } { x } \)

USing first principle prove that \( y=\sin x \) then \( \frac{d y}{d x}=\cos x \)

8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \).

Suppose \( f \) is continuous on \( [1,5] \) and the only solutions of the equation \( f(x)= \) 6 are \( x=1 \) and \( x=4 \). If \( f(2)=8 \), explain why \( f(3)>6 \). Show that \( F(x)=|x| \) is continuous evervwhere.