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Find derivatives of sine and cosine functions

Let it be known that\newlinelim⁡x→1f(x)=+∞,lim⁡x→1g(x)=−∞,lim⁡x→1v(x)=0,  \lim _{x \rightarrow 1} f(x)=+\infty, \lim _{x \rightarrow 1} g(x)=-\infty, \lim _{x \rightarrow 1} v(x)=0 \text {, } \newlineFind the values of the following limits:\newline11) lim⁡x→1(f(x)−5g(x)) \lim _{x \rightarrow 1}(f(x)-5 g(x)) ;\newline22) lim⁡x→1(f(x)+v(x)) \lim _{x \rightarrow 1}(f(x)+v(x)) ;\newline33) lim⁡x→1(g(x)+v(x)) \lim _{x \rightarrow 1}(g(x)+v(x)) ;\newline44) lim⁡x→11g(x) \lim _{x \rightarrow 1} \frac{1}{g(x)} ;\newline55) lim⁡x→1v(x)f(x) \lim _{x \rightarrow 1} \frac{v(x)}{f(x)} ;
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Let it be known that\newlinelim⁡x→1f(x)=+∞,lim⁡x→1g(x)=−∞,lim⁡x→1v(x)=0,  \lim _{x \rightarrow 1} f(x)=+\infty, \lim _{x \rightarrow 1} g(x)=-\infty, \lim _{x \rightarrow 1} v(x)=0 \text {, } \newlineFind the values of the following limits:\newline11) lim⁡x→1(f(x)−5g(x)) \lim _{x \rightarrow 1}(f(x)-5 g(x)) ;\newline22) lim⁡x→1(f(x)+v(x)) \lim _{x \rightarrow 1}(f(x)+v(x)) ;\newline33) lim⁡x→1(g(x)+v(x)) \lim _{x \rightarrow 1}(g(x)+v(x)) ;\newline11\newline44) tim⁡x→1g(x) \operatorname{tim}_{x \rightarrow 1} g(x) \newline55) lim⁡x→1v(x)f(x) \lim _{x \rightarrow 1} \frac{v(x)}{f(x)} ;
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44) أي مما يلي يصف السلوك الطرفي للرسم البياني للاالة\newlinea) lm⁡x→−∞f(x)=∞,lim⁡x→∞f(x)=−∞ \operatorname{lm}_{x \rightarrow-\infty} f(x)=\infty, \lim _{x \rightarrow \infty} f(x)=-\infty \newlineb) lim⁡x→−∞f(x)=∞,lim⁡x→∞f(x)=∞ \lim _{x \rightarrow-\infty} f(x)=\infty, \lim _{x \rightarrow \infty} f(x)=\infty \newlinec) lim⁡x→−∞f(x)=−∞,lim⁡x→∞f(x)=−∞ \lim _{x \rightarrow-\infty} f(x)=-\infty, \lim _{x \rightarrow \infty} f(x)=-\infty \newlined) lim⁡x→−∞f(x)=−∞,lim⁡x→∞f(x)=∞ \lim _{x \rightarrow-\infty} f(x)=-\infty, \lim _{x \rightarrow \infty} f(x)=\infty
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22.We have p=3,x1=[20]x2=[01]y1=1y2=2 p=3, x_{1}=\left[\begin{array}{l}2 \\ 0\end{array}\right] x_{2}=\left[\begin{array}{l}0 \\ 1\end{array}\right] y_{1}=1 \quad y_{2}=2 , setting λ=0.001 \lambda=0.001 , try to compute\newline[w0w]=A−1bA=[p∑i=1pxiT∑i=1pxi(∑i=1pxixiT)+λnn×n]⋅b=[∑i=1pyi∑i=1pyixi \left[\begin{array}{l} w_{0} \\ w \end{array}\right]=\mathbf{A}^{-1} \mathbf{b} \quad \mathbf{A}=\left[\begin{array}{cc} p & \sum_{i=1}^{p} x_{i}^{T} \\ \sum_{i=1}^{p} \mathbf{x}_{i}\left(\sum_{i=1}^{p} \mathbf{x}_{i} \mathbf{x}_{i}^{T}\right)+\lambda \mathbf{n}_{n \times n} \end{array}\right] \cdot \mathbf{b}=\left[\begin{array}{c} \sum_{i=1}^{p} y_{i} \\ \sum_{i=1}^{p} y_{i} \mathbf{x}_{i} \end{array}\right.
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The function f f is given by f(x)=5x6−2x3−3 f(x)=5 x^{6}-2 x^{3}-3 . Which of the following describes the end behavior of f f ?\newline(A) lim⁡x→−∞f(x)=−∞ \lim _{x \rightarrow-\infty} f(x)=-\infty and lim⁡x→∞f(x)=−∞ \lim _{x \rightarrow \infty} f(x)=-\infty \newline(B) lim⁡x→−∞f(x)=∞ \lim _{x \rightarrow-\infty} f(x)=\infty and lim⁡x→∞f(x)=∞ \lim _{x \rightarrow \infty} f(x)=\infty \newline(C) lim⁡x→−∞f(x)=−∞ \lim _{x \rightarrow-\infty} f(x)=-\infty and lim⁡x→∞f(x)=∞ \lim _{x \rightarrow \infty} f(x)=\infty \newline(D) lim⁡x→−∞f(x)=∞ \lim _{x \rightarrow-\infty} f(x)=\infty and lim⁡x→∞f(x)=−∞ \lim _{x \rightarrow \infty} f(x)=-\infty
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