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Home Question Bank Math Calculus Archive 2024 December 30

Calculus Questions from Dec 30,2024

Browse the Calculus Q&A Archive for Dec 30,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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4. 000 Calcula els limits següents mitjançant taules de va- lors: \( \begin{array}{ll}\text { a) } \lim _{x \rightarrow 0} \frac{x-1}{x-5} & \text { b) } \lim _{x \rightarrow-2} \frac{x^{2}-4}{x+2} \\ \text { Sol.: a) } 1 / 5: \text { b) }-4\end{array} \) Identify the horizontal asymptote of the function \( f(x) = 3 e^{-x} + 5 \). \[ g(x)=\frac{3}{x} \] \( T_{g}(a, b)=\frac{f(a)-f(b)}{a-b} \) \( f(a)=\frac{3}{a} \quad f(b)=\frac{3}{b} \) Calculer taux d'accraissement \( T_{g}(a, b) \) \[ g(x)=\frac{3}{x} \] \( T_{g}(a, b)=\frac{f(a)-f(b)}{a-b} \) \( f(a)=\frac{3}{a} \quad f(b)=\frac{3}{b} \) Calculer taux d'accraissement \( T_{g}(a, b) \) \( f(x)=-2 x^{2}+4 \) \( T_{f}(a, b)=\frac{f(a)-f(b)}{a-b} \) \( f(a)=-2 a^{2}+4 \quad f(b)=-2 b^{2}+4 \) Calculer taux d'accroissement \( T_{f}(a, b) \) Et étudier le sens de variation de \( f \) sur l'intervalle \( [0,+ \) infinie [ et ]- infinie ; 0 ] 10. \( \int_{e}^{e^{2}}\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^{2} d x= \) (A) \( \frac{e^{4}}{2}+2 e^{2}+2 \) (B) \( \frac{e^{2}}{2}+2 e+1 \) (C) \( e^{4}+2 e^{2}+e \) (D) \( \frac{e^{4}}{2}+\frac{3 e^{2}}{2}-2 e+1 \) (E) \( \frac{e^{4}}{2}+e^{2}+e \) (Beci (B) \( \int \frac { x + 2 } { x ( x ^ { 2 } + x + 1 ) } d x = \int \) \( h(x)=\sqrt{x-3} \) Calculer taux d'accroissement de \( T_{h}(b ; a) \) \( f(a)=\sqrt{a-3} f(b)=\sqrt{b-3} \) \( T_{h}(a, b)=\frac{(\sqrt{a-3})-(\sqrt{b-3})}{a-b} \) \( \int _ { 0 } ^ { \infty } E d m \quad , \quad E = \sqrt { p ^ { 2 } \cdot c ^ { 2 } + m ^ { 2 } \cdot c ^ { 2 } } \) Evaluate the indefinite integral \( \int \frac{\ln x}{x} d x \)
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