Calculus Archive: Questions from September 18, 2022
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please do 22 26 & 30 only thank you
At what points are the functions in Exercises 13-30 continuous? 13. \( y=\frac{1}{x-2}-3 x \) 14. \( y=\frac{1}{(x+2)^{2}}+4 \) 15. \( y=\frac{x+1}{x^{2}-4 x+3} \) 16. \( y=\frac{x+3}{x^{2}-3 x-10} \)1 answer -
\( 1.1 \int \frac{\tan x \sec ^{2} x}{3+\tan ^{4} x} d x \) \( 1.2 \int \frac{e^{\sin ^{-1} x}}{\sqrt{1-x^{2}}} d x \) \( 1.3 \int \frac{1}{x+x \ln x} d x \) 2 Determine the following integrals \( 2.11 answer -
number 19 please
In Problems 15-20, find dy for each function. 15. \( y=30+12 x^{2}-x^{3} \) 16. \( y=200 x-\frac{x^{2}}{30} \) 17. \( y=x^{2}\left(1-\frac{x}{9}\right) \) 18. \( y=x^{4}\left(150-x^{3}\right) \) 19.1 answer -
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I. Aplique los procesos estudiados para resolver problemas de valor inicial para obtener la solución particular de acuerdo a las condiciones dadas por el ejercicio. a) Determine \( f(x) \) para \( f^1 answer -
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6) Find the solution of the following initial value problems. a) \( y^{\prime \prime}+2 y^{\prime}=3+4 \sin t, y(0)=0, y^{\prime}(0)=6 \). b) \( y^{\prime \prime}+5 y^{\prime}+6 y=\cos t, y(0)=5, y^{\1 answer -
Match the functions with the graphs of their domains. 1. \( f(x, y)=\ln (x+y) \) 2. \( f(x, y)=e^{\frac{1}{x+y}} \) 3. \( f(x, y)=\sqrt{x^{5} y^{2}} \) 4. \( f(x, y)=x+y \)1 answer -
use the quotient rule to find the derivative of the following- #13, 15,21,23
13. \( y=\frac{5-3 t}{4+t} \) 14. \( y=\frac{9-7 t}{1-t} \) 15. \( y=\frac{x^{2}+x}{x-1} \) 16. \( y=\frac{x^{2}-4 x}{x+3} \) 17. \( f(t)=\frac{4 t^{2}+11}{t^{2}+3} \) 18. \( y=\frac{-x^{2}+8 x}{4 x^{1 answer -
Find the horizontal asymptote(s) for \( f(x)=\frac{\sqrt{4 x^{2}+7}}{8 x+6} \). A. \( y=\frac{1}{4} \) B. \( y=\frac{1}{2} \) C. \( y=-\frac{1}{2} \) and \( y=\frac{1}{2} \) D. \( y=-\frac{1}{4} \) an2 answers -
28 show work with explanations
23-38 = Differentiate the function. 23. \( f(x)=x^{5}+5^{x} \) 24. \( g(x)=x \sin \left(2^{x}\right) \) 25. \( f(t)=10^{\sqrt{t}} \) 26. \( F(t)=3^{\cos 2 t} \) 27. \( L(v)=\tan \left(4^{v^{2}}\right)1 answer -
35 show all work and explain
23. \( f(x)=x^{5}+5^{x} \) 24. \( g(x)=x \sin \left(2^{x}\right) \) 25. \( f(t)=10^{\sqrt{t}} \) 26. \( F(t)=3^{\cos 2 t} \) 27. \( L(v)=\tan \left(4^{v^{2}}\right) \) 28. \( G(u)=\left(1+10^{\ln u}\r1 answer -
parts a-c
Find the derivative for \( f(x) \) or \( y \) '. \( \begin{array}{lll}\text { a. } & y=(\cos x)^{x+1} f(x) \text { or } y^{\prime} & \text { ANS: }(\cos x)^{x+1}(\ln (\cos x)-(x+1) \tan x) \\ \text {2 answers -
parts h-j
Find the derivative for \( f(x) \) or \( y \) '. \( \begin{array}{lll}\text { a. } & y=(\cos x)^{x+1} f(x) \text { or } y^{\prime} & \text { ANS: }(\cos x)^{x+1}(\ln (\cos x)-(x+1) \tan x) \\ \text {1 answer -
#72, not 71
\( -72 \) Describe how the graph of \( g \) is obtained from the graph of \( f \). \( 1 . \) a. \( g(x, y)=f(x, y)+2 \) b. \( g(x, y)=2 f(x, y) \) c. \( g(x, y)=-f(x, y) \) d. \( g(x, y)=2-f(x, y) \)2 answers -
Solve the separable initial value problem. 1. \( y^{\prime}=2 x \cos \left(x^{2}\right)\left(1+y^{2}\right), y(0)=2 \Rightarrow y= \) 2. \( y^{\prime}=\ln (x)\left(1+y^{2}\right), y(1)=2 \Rightarrow y2 answers -
answer all questions
(a) \( y=t^{\sqrt{t}} \) (b) \( y=\frac{(2 x+2)^{2}(3 x+4)^{3}}{(x-3)^{8}} \) (c) \( g(x)=\ln \frac{3-x}{3+x} \) (d) \( y=\sqrt[4]{\frac{x^{2}+1}{x^{2}-1}} \)1 answer -
The largest set on which the funtion \( f(x, y)=\sqrt{x+y}-\sqrt{x-y} \) is continuous is A. \( \{(x, y) \mid x \geq y\} \) B. \( \{(x, y) \mid-x1 answer -
5. [6 pts.] Solve the initial value problem \[ (y \tan x-\sin 2 x) d x+d y=0, y(0)=1 \] A. \( y=3 \cos x-2 \cos ^{2} x \) C. \( y=2 \cos x-3 \cos ^{2} x \) B. \( y=3 \cos x+2 \cos ^{2} x \) D. \( y=21 answer -
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\( f(x)=\left\{\begin{array}{cc}x \sin \frac{1}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \)1 answer -
Please write it in neat handwriting,thanks a lot
At what points are the functions in Exercises \( 13-30 \) continuous? 13. \( y=\frac{1}{x-2}-3 x \) 14. \( y=\frac{1}{(x+2)^{2}}+4 \) 15. \( y=\frac{x+1}{x^{2}-4 x+3} \) 16. \( y=\frac{x+3}{x^{2}-3 x-1 answer -
23. \( y+5 x^{2}=7 \) 27. \( y-x^{2}+2=10-x^{2} \) In Problems 21-28, each equation specifies a function with independent variable \( x \). Determine whether the function is linear. constant, or neit2 answers -
Given \( y=4 \cos (\theta)+10 \sin (\theta) \), find \( \left.\frac{d^{2} y}{d \theta^{2}}\right|_{\theta=\pi}=? \)1 answer -
Find \( y^{\prime}: \) \[ y=(5 x-4)\left(2 x^{3}-x^{2}+1\right) \] A) \( 30 x^{3}+39 x^{2}-13 x+5 \) B) \( 13 x^{2}-39 x+5 \) C) \( 10 x^{3}+13 x^{2}-39 x+5 \) D) \( 13 x^{2}+5 \) E) \( 40 x^{3}-39 x^1 answer -
FYnd the derivative. \[ y=\frac{8}{\sin (x)}+\frac{1}{\cot (x)} \] A) \( y^{\prime}=8 \csc (x) \cot (x)-\csc ^{2}(x) \) B) \( y^{\prime}=-\csc (x) \cot (x)+8 \sec ^{2}(x) \) c) \( y^{\prime}=-8 \csc (1 answer -
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31-34 Find \( f^{\prime}(x) \) and \( f^{\prime \prime}(x) \). 31. \( f(x)=x^{2} e^{x} \) 32. \( f(x)=\sqrt{x} e^{x} \) 33. \( f(x)=\frac{x}{x^{2}-1} \) 34. \( f(x)=\frac{x}{1+\sqrt{x}} \) 1-54 Use t2 answers -
2. Find \( \frac{d y}{d x} \) for each of the following: (a) \( y=\cos ^{3}(2 x+1) \) (e) \( y=\frac{x^{3}}{\cos x} \) (b) \( y=\sec (2 x+1)^{3} \) (f) \( y=\sin \left(\frac{1}{2 x-1}\right) \)2 answers -
10. Find \( \frac{d z}{d t} \) where \( z=3 x^{2} y^{3}, x=t^{4} \) and \( y=t^{2} \) 11. Given \( f(x, y, z)=x y z \), find \( f_{x y y} \) 12. Given \( f(x, y, z)=x y z \), find \( f_{y x y} \) 13.2 answers -
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