1. Get the first derivative f': 2. Find the factors: 3. Find the critical numbers: 4. Get the second derivative f": 5. Find the factors: 6. Find the critical numbers: 7. Draw a number line and plot (not to scale) all the critical numbers arranged in as- cending order: 8. Make the table similar to what is shown below. Create rows for the intervals and critical numbers. 9. Choose values of c from the intervals: 10. Compute the function values for the critical numbers: 11. Note f'(x) = 0 for x = -},1 and f"(x) = 0 for x = -ž,1. Write 0 accordingly. 12. Fill out other values for the column for f' and f". Exact values can be provided but the SIGNS are already sufficient and more important. 13. Draw conclusions 14. Sketch the graph.

Q: 2. Evaluate xy(z + 2) dx dy dz

A:

Q: Using Wallis formula, find the integral of the expression. Answer in 5 decimal places (example…

A: We have to solve given integration with the help of wallis formula.

Q: tan e de sece+ 4 cos € COS

A: The given integral is tan(phi)/[sec(phi)+4cos(phi)]

Q: y''  +  y'+  2y  =  3e^2x

A:

Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

A:

Q: finfyiy-6)"dy 2. 2.

A: We have to solve given integral.

Q: dx kx, x(t,)=x, dt where k is a constant of proportionality, serves as a model for diverse phenomena…

A: Topic:- function

Q: 1. Let z = 3+ 6i and w = a + bi where a, b e R. Without using a calculator, (a) determine , and…

A: Let's find ratio of given complex numbers.

Q: Find the inverse laplace transform of the function

A:

Q: 1) Find the Taylor series for f(x) = ln x centered at 3. Show All Your Work.

A:

Q: x² – 2 (x + 2)(x + 1)² 1 + x + 2 x + 2 (x + 1)? x + 1 (x + 1)² Option 1 Option 2 1 1 2 1 x + 2 x +1…

A: The given expression is; x2-2x+2x+12   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: Use the Divergence Theorem to evaluate F N dS and find the outward flux of F through the surface of…

A: See is solution

Q: Find the work done by winding 3 meters of a cable if the force applied to wind the cable by x meters…

A:

Q: (D- 3)'( D + 9)y = 0

A: We can solve the give ODE as follows:

Q: 3.f(x) = (2x+3 if x =1 2 if x=1 4. (x)= {3+x if x s1

A: (3)f(x)=2x+3 if  x≠12     if  x=1limx→1-f(x)=limx→1-2x+3=5limx→1+f(x)=limx→1+2x+3=5f(1)=2it is…

Q: xydy – (y 3x2) dx = 0 –

A:

Q: 2. Find the equation of the normal line to the graph of y = x(1+ In x) at x = e. Write your answer…

A:

Q: ydy -ヌ-9-y 7-8. 2.

A:

Q: dy Find Y dx (x- 2) - (2x+1)4 if y= | Use logarithmic differentiation. x=0 e2x. Vx+8

A:

Q: Jy ニ0 (y cosxy +1) dx + z0- (xcosty +2y=3) dy

A:

Q: 3. (a) y(8) when y=cos 2x

A:

Q: Find the first derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and y = ( ex – e –x ) / (ex…

A:

Q: (x +y) dx +(x+y)dy z o

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Discuss the symmetry of the graph of each polynomial function. 1. f(x)=2x 3. f(x)=-x' 5. f(x)=(x-3)*…

A: Given Polynomial f(x)=2x f(x)=x2+1 f(x)=-x3 f(x)=x4-x

Q: x + 2 x + 1

A: ∫x2+2x+1dxSubstitute u=x+1→dudx=1→dxu=dxx2=(u-1)2 =∫(u-1)2+2udu=∫u+3u-2du

Q: Solve the equation (D² – 3D + 2) y = 2e¬* + 8 O y = cje2x + C2xe¯* + 4 + ze* O y = cje2x + cze² + 4…

A:

Q: -2 Find f'(x). Given: f (x) = (2x3+3x2-5)2

A:

Q: 1 11. lim, -2 Inx x-1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: Given;  Radius=9cm dr/dt=0.4 cm/min

Q: Supply the missing integrand and the limits of integration dx dy _dy ху

A: The given integral:∫-11∫1eydxdyxy

Q: 09. lim, " -т(csc Tх) (Inx)| x)(Inx)]

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A. Given f(x) = x³ - 4x2- 4x + 16, find; a. Zeros of the function b. Critical numbers c. local…

A:

Q: Determine the exact solution of the following differential equation y =2- y at y(0) -1. So the value…

A:

Q: e* (1-e*) (1+х) [Iin(1-х)] 12. lim,»0

A: LetL=limx→ 0ex1-ex1+xln1-xplug x=0L=e01-e01+0ln1-0L=11-11ln1L=1.01.0L=00Which is undetrminat…

Q: Find the equation of the parabola with the given properties Vertex (0,0), focus (5, 0). = x

A:

Q: find the Fourier series of the following equation -1<x<0 (-) f(x) = }x 0 <x<1 1<x <3

A: Given

Q: The volume, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is 100n 100/9…

A:

Q: 2. Use membership tables to prove that A - (BnC) = (A – B) U (A – C).

A:

Q: 10. In writing a function in the denominator and its derivative is in the numerator, which of the…

A:

Q: Assignment On Integral of Exponential & Logarit Determine the integral of the ff. functions. 1. S -…

A:

Q: 5. S 7x°csc²3x7 dx du = answer:

A:

Q: Solution: Here * = Sin x The graph is Ine Shadded negion find i The required of we have to the area…

A: Let's find  area of given curves y=e^x from x=0 to x=1.

Q: 8) Find the slope of the curve y = Sin³0 and x = Cos³0 _when 0 =

A: Given y=sin^2(theta), x=cos^3(theta)

Q: х3-4х-10 х2-х-6 (2x + 21n|x – 31 – 4 In |x + 2|) + C (2x + 2 In|x – 3| + 4 In |x + 21) + C Option 1…

A:

Q: x2 (x+2)³ In Ix + 21 + 4x+6 4x+6 (x+2)= In |x + 2| – (x+2)= +C Option 1 Option 2 ihk+ 21- 4x+6 In lx…

A:

Q: 1. Solve the equation: (4D4 – 4D³ – 23D² + 12D + 36) y = 0 O y = cje* + c2xe2" + c3e¯7 + c4xe¯i O y…

A: The given equation is: (4D4-4D3-23D2+12D+36)y=0...(1)

Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

A:

Q: 8. If y = (x* +2x²)e2* determine an expansion for y(5). %3D [y(5) = e2x24(2x³ + 19x² + 50x + 35)]

A:

Q: sec =zydy

A: Given

Q: Find the derivative of the following function F(x) (2t – 1)' dt

A: To find the derivative of the following function.Fx=∫x2x72t-13 dt