Compute the average value of \( f(t) = \sin(t) + \cos(t) \) over the interval \([0, \pi]\).

tvo: Work out Find the quadratic approximation of the function \( \sqrt{1}+x \) at \( \times \) close to 0 ?

Determine the distance traveled by a particle moving along the curve \( y = \sin(x) \) from \( x = 0 \) to \( x = \pi \).

If \( \left\langle a_{n}\right\rangle \) and \( \left\langle b_{n}\right\rangle \) are two sequences such that \( \lim _{n \rightarrow \infty} a_{n}=i, \lim _{n \rightarrow \infty} b_{n}=m \), then prove that: \( \lim _{n \rightarrow \infty}\left(a_{n}+b_{n}\right)=l+m \)

\( \left. \begin{array} { l } { f ^ { \prime } ( x ) = 4 \sqrt { x ^ { 3 } } + k x ^ { - 2 } } \\ { f ^ { \prime \prime } ( x ) = } \end{array} \right. \)

\( \left. \begin{array} { l } { f ^ { \prime } ( x ) = 4 \sqrt { x ^ { 3 } } + k x ^ { - 2 } } \\ { f ^ { \prime \prime } ( x ) = } \end{array} \right. \)