Calculus Archive: Questions from August 27, 2022
-
1 answer
-
1 answer
-
13. Evaluate the limit (a) \( \lim _{x \rightarrow 0} \frac{\sqrt{1+\sin ^{2}\left(x^{2}\right)}-\cos ^{3}\left(x^{2}\right)}{x^{3} \tan x} \)1 answer -
1 answer
-
En la siguiente gráfica se muestran \( f, f^{\prime} \) y \( f^{\prime \prime} \) en el mismo plano cartesiano. ¿Cuál es cuál? Explique su razonamiento.|2 answers -
1 answer
-
g) \( \int\left(\theta^{2}+\sec ^{2} \theta\right) d \theta \) h) \( \int\left(\sec y \tan y-\csc ^{2} y\right) d y \). i) \( \int \cos ^{6}(8 x) \sin (8 x) d x \).1 answer -
3 answers
-
\( \lim _{x \rightarrow 1} f(x) \) \( f(x)=\left\{\begin{array}{ll}x^{2}+3, & x \neq 1 \\ 2, & x=1\end{array}\right. \)1 answer -
Use the chain rule in each: a) If w = f (u, v) and in turn u = g (x, y, z) and v = h (x, y, z), establish formulas for : b) If z = f (u) and in turn u = g (x, y), establish formulas for: Original Do
\( \frac{\partial \boldsymbol{w}}{\partial \boldsymbol{x}}, \quad \frac{\partial \boldsymbol{w}}{\partial \boldsymbol{y}} \quad \) y \( \quad \frac{\partial \boldsymbol{w}}{\partial \boldsymbol{z}} \)1 answer -
Find \( \frac{d y}{d x} \) for the following expressions: a) \( y=x^{3} \ln (3 x) \) b) \( y=2 \sin \left(\frac{1}{x}+2 x^{2}\right) \) c) \( y=\frac{2 x^{3}+7 x+\sin (x)}{\cos (2 x)} \) d) \( 3 x^{3}1 answer -
1 answer
-
Consedere the limit Use a graphical calculator to find the limit. Find the limit analytically.
re el límite \( \lim _{x \rightarrow 0^{+}}(\cos x)^{1 / x^{2}} \) a. Use una calculadora gráfica para hallar el límite. b. Encuentre el límite analíticamente.2 answers