Get questions and answers for Calculus

Calculus Archive: Questions from September 23, 2022

• Find dy/dx
  \[ y=\ln \cos 4 x \] \( y=e^{x} \ln x \) \[ y=\ln \left(4^{x}\right) \]
  2 answers
• 
  

  
  II. Use the polar coordinates to write and evaluate the doble integral. \[ \int_{R} \int f(x, y) d A \] Para \( f(x, y)=x+y \) donde \( R: x^{2}+y^{2} \leq 4, x \geq 0, y \geq 0 \)
  2 answers
• 
  

  
  If \( y=3 \sin x+x^{2} \cos x \), find \( \left.\frac{d^{2} y}{d x^{2}}\right|_{x=\frac{\pi}{4}} \) \( -1.345 \) \( -2.385 \) \( -4.225 \) \( -3.365 \)
  1 answer
• 10,16,22,30 please and thank you
  Finding a Derivative In Exercises 9-34, find the derivalur of the function. 9. \( y=(2 x-7)^{3} \) 10. \( y=5\left(2-x^{3}\right)^{4} \) 11. \( g(x)=3(4-9 x)^{5 / 6} \) 13. \( h(s)=-2 \sqrt{5 s^{2}+3}
  1 answer

• 

  
  If \( \sin x=-\frac{1}{4} \) and \( \tan y=\frac{2}{5} \) where \( x \) and \( y \) are in the interval \( [\pi / 2,3 \pi / 2] \), What are the exact values of the following trigonometric ratios? (Mat
  2 answers

• 

  
  Find \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) for \( f(x, y)=-8 x-4 x y+8 y \)
  2 answers

• 

  
  If \( \sin x=-\frac{1}{4} \) and \( \tan y=\frac{2}{9} \) where \( x \) and \( y \) are in the interval \( [\pi / 2,3 \pi / 2] \), What are the exact values of the following trigonometric ratios? (Mat
  2 answers
• 
  

  
  Find the total differential of \( z=f(x, y) \) where \[ f(x, y)=\int_{0}^{x}\left(2 t^{3}-\cos (2 t)\right) d t+\ln \left(\left(\frac{y}{x}\right)^{3}\right. \] \( d z= \)
  3 answers

• 

  
  Solve the initial value problem \[ y y^{\prime}=\frac{5 x^{2}+1}{y} ; y(0)=2 \]
  2 answers
• 
  

  

  

  
  Find \( \frac{d^{2} y}{d x^{2}} \) \[ y=5 x+3 \] \( \frac{d^{2} y}{d x^{2}}= \) Find \( f^{\prime \prime}(x) \) \[ f(x)=\left(x^{2}+3\right)^{4} \] \[ f^{\prime \prime}(x)= \] For the function \( y=
  2 answers

• 

  
  I. Considere \( w=x^{2}-2 x y+y^{2}, x=r+\theta, y=r-\theta \) para determinar \( \frac{\partial w}{\partial r} \& \frac{\partial w}{\partial \theta} \). II. Considere \( w=x y \cos (z), x=t, y=t^{2}
  2 answers

• 

  
  Match each graph to the correct equation. Equations: I Graph F) Graph E) Graph B) Graph A) Graph C)
  2 answers
• 
  

  
  Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=e^{\alpha x} \sin (\beta x) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]
  2 answers

• 

  
  If \( y^{\prime \prime}=\frac{1}{(x+1)^{2}}, y(0)=2, y^{\prime}(0)=1^{\text {then }} y^{\prime}= \) and \( y= \)
  2 answers
• find y' and y"
  Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\cos \left(x^{2}\right) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]
  2 answers
• Both parts
  Establezca y evalúe el integral en las coordenadas más convenientes para determinar el área de la región. A. B.
  0 answers
• 
  

  
  For \( f(x, y)=x^{2} y^{4}-3 x^{4} y \), calculate \( f_{x x x}(x, y) \) \[ \begin{array}{l} f_{x x x}(x, y)=12 x^{2} y \\ f_{x x x}(x, y)=-3 x y \\ f_{x x x}(x, y)=-72 x y \\ f_{x x x}(x, y)=-36 x y
  1 answer
• 
  

  
  Differentiate. \[ y=9 x^{2} \sin (x) \tan (x) \] \[ y^{\prime}= \]
  1 answer
• ​​​​​​​
  8. Dada la integral de área: \[ J=\int_{R} x^{2} d A \] en donde \( R \) es la región del primer cuadrante del plano \( X Y \) limitada por la hipérbola \( x y= \) 16 y las tres rectas \( y=x, y=0
  1 answer
• 
  

  
  \( y=x^{2} \) and \( y=-2 x^{2}+3 \)
  1 answer
• 1) find the domain and range of it .. 1) y = |f(x)| 2) y = f(x − 3) + 1 3) y = f (1/2x) (d) y = f(x + 2) − 3 (e) y = f(−x) (f) y = −f(x)
  0 answers
• 1) find the domain and range of it .. 1) y = |f(x)| 2) y = f(x − 3) + 1 3) y = f (1/2x) (d) y = f(x + 2) − 3 (e) y = f(−x) (f) y = −f(x)
  0 answers
• 
  

  

  
  If \( f(x)=x^{2}-7 x \), find: \[ f(a+1)-f(a)= \] If \( f(x)=8 x^{2} \), find: \[ f(4+h)-f(4)= \]
  2 answers
• find y' please
  51. \( y=\sin (\pi x)^{2} \)
  2 answers

• 

  
  If \( y=a \sin (2 x)-b \cos (2 x) \) Prove that \( \left(y^{\prime}\right)^{2}+4 y^{2}=4\left(a^{2}+b^{2}\right) \)
  2 answers