Find 2he tangentline at \( x_{0}=1 \) \( y=x e^{x} \)

If \( \phi \) and \( \psi \) are differentiable scalar functions of position \( x, y, z \) then \( \operatorname{grad} \phi+\psi \) is equal to Select one: \( \operatorname{div} \phi+\psi \) \( \operatorname{curl} \phi+\psi \) \( \operatorname{grad} \phi+\operatorname{grad} \psi \) \( \operatorname{div} \phi+\operatorname{div} \psi \)

(6) \( \int \mathrm{e}^{\ln x} \mathrm{~d} x=\ldots \ldots \ldots \ldots+c \) \( \begin{array}{llll}\text { (a) } \frac{x^{2}}{2} \ln x & \text { (b) } \ln x & \text { (c) } \frac{1}{2} x^{2} & \text { (d) } \mathrm{e}^{x}\end{array} \)

53) \( \lim _{x \rightarrow \frac{\pi}{3}} \frac{2 \cos x-1}{\sqrt{3}-\tan x} \)

If A is differentiable vector function, then \( \nabla \times \nabla \times A \) Select one: \( \nabla \nabla \cdot A-\nabla^{2} A \) 0 \( \nabla^{2} A \) \( \nabla \nabla \cdot A \)

41) \( \lim _{x \rightarrow \pi}\left(x^{2}-\pi^{2}\right) \tan \frac{x}{2} \)