Sketch a graph of a polynomial function that meets all of the following conditions: 3 is a zero of multiplicity 1, -1 is a zero of multiplicity 2, and 1 is a zero of multiplicity 2. There are no other zeros. P(0)=6 The leading coefficient of P is -2. D

Q: thi Prove that the improper integral } ] docdy (1 + x² + y²) ³¹²/₂ Converges

A:

Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (7x²2) to…

A: Maclaurin series of sin(x) :              sin(x) = x-x33!+x55!-x77!+...

Q: 2. Find the Maclaurin series of f(x) = tanh-¹x

A: Note: according to our guidline i can solve only first please reroute the remaining question.  Find…

Q: Find the derivative of V(x) = ln(sin x) – (x4 – 3x)10

A: We can find the derivative as below.

Q: A spherical water tank 1 ft in radius, has a spout of length 1 ft at the top of the tank, is full of…

A: Given problem:- A spherical water tank 1 ft in radius, has a spout of length 1 ft at the top of the…

Q: Differentiate and simplify this function g (y) = y3 / ln(2y)

A:

Q: Question 1 CD Assume that "Foo is a function defined by Foo = x²-3x+1 288-1 For a ≤x≤3 Prove that…

A: Given: fx = x2-3x+12x-1---------------------------------To prove: Fx is bounded for 2≤x≤3.…

Q: x-y (x,y) →(0.0) x + y 2.) Prove that lim does not exist.

A:

Q: P-4 Use separation of variables to find the product solution of the following a) ди ди b) J2u 02u y…

A:

Q: Convert the rectangular coordinates (4, 0) into polar form. Express the angle using radians in terms…

A:

Q: Suppose 8 3n f(x) = n! (x - 7) n n=0 7 To determine So f(x) dx to within 0.0001, it will be…

A: We have to find the value of integral.

Q: ib Show that the function defined by F(x, y) xy √² + y² O is not differentiable at point (0,0) if…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

A:

Q: 8 34) 2xe-x² dx <80 A) Convergent B) Divergent

A:

Q: 1000 1+9e-t The number of minnows in a back yard pond is modelled by the equation P(t) = Where is…

A:

Q: Find the transition points. y = 2x6 - 18x4 (Use symbolic notation and fractions where needed. Give…

A:

Q: Let A(z) = f(t)dt, with f(x) shown in the graph below. N -2- At what x values does A(x) have a local…

A: Ax=∫0xftdt, with f(x) shown in the graph.

Q: Given plane z: 3x+2y+=-3=0, point P(1, -2, 3), and lines 1₁:¹¹ and 4₂: (3, 6,-5)+r(2, 3, 1), find:…

A:

Q: (b) Show that the interval of convergence of the series n=1 sest 2-12-1 (4n-3)² is given by

A:

Q: 10-x-x² if x 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

A:

Q: 21. Jo 0 dx (x + 1)(x² + 1)

A:

Q: Let C be the circle with radius 3 centered at the origin, oriented counterclockwise. Define a vector…

A:

Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: Evaluate the following integrals: dx dx a. S b. f √81+16x² √16x²-9 C. S dx 49-4x²

A:

Q: y = e²x and x - 2y + 5 = 0

A: x-2y+5=02y=x+5y=x+52The equations are: y=x+52y=e2x

Q: Calculate the area contained between the curve y = cos x, π<x< , and the line y =

A: Given:-y=cosx, -π&lt;x&lt;πy=1/2

Q: problem: Find the vector below. ting the unit normal vector of A = 40 + 7 ₁ 0 - 3 K

A:

Q: to onuabjanip 2+1 (-1) 7-1 Jo to - 두 + 두 Soudbranvol - 1 Prove the

A:

Q: A sketch of the region enclosed by y = x and y = f Area of the region = fot 4.25 2²+1 follows.

A: Given: y=x and y=4.25xx2+1 First find the intersection point Thus, x= 4.25x1+x2 ⇒1+x2= 4.25⇒x=…

Q: Let f(x) = In(64x2 + 16x + 26). (If an answer does not exist, enter DNE.) (a) Find the interval(s)…

A:

Q: What is an equation for the cosine graph shown below? -135 -90 -45 -11 -10 +9 8/ -7 -6 -5 3 2 1 45…

A: Given query is to find the cosine equation of the function.

Q: Evaluate the integral. (Use C for the constant of integration.) ] = 5 tan(x) sec³(x) dx

A: The given integration is: ∫5tanxsec3xdx To find the value of integration.

Q: how to prove that a and b are divisible by d if and only if au+bv is divisible by d. a,d,u,v,b are…

A:

Q: Let f(x, y) = 2x and C be the line segment on the plane from (0, 0) to (3, 4). Evaluate the line…

A:

Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

A:

Q: 2 OM a) Find the area of the region b) Find the length of the curve c) Find the surface area generat…

A: A detailed solution is given below.

Q: 4) A headboard for a bed is built in the shape of a semielliptical arch. The headboard will be 8…

A: Given; a=4, b=3

Q: T -2 -1 4 3 2 - -3 1 3. From the above graph of y = f(x), find the following limits: (a) lim f(x) =…

A: (a)  limx→-4f(x)=2   (b)  limx→-3f(x)=-2   (c)  limx→-2f(x)=-3   (d)  limx→1f(x)=infinite

Q: ol Down: Two Reflections . Graph the function g given by g(x) = -f(x). 2. Graph the function h given…

A: Reflection

Q: Set up the definite integral required to find the area of the region between the graph of y= 2²-12…

A: find intersection point

Q: 2. Evaluate x sin ædr using integration by parts.

A: Given: I=∫xsinxdx   We know the basic integration formula. ∫sinxdx=-cosx+C∫cosxdx=sinx+C

Q: (A) (в Identify the form of the partial fraction decomposition of the rational function -3² +10…

A:

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: A(4) = A'(4) -

A: Integration gives area below curve area above x axis is positive area below x axis is negative A(4)…

Q: 8) Determine p'(x) where P(x) = 0.08e*

A:

Q: Find the area contained between the two curves y = 3x - x² and y=x+x². 1/3 sq. units 1/4 sq. units…

A:

Q: that the internal of Convergence of the server 24-12-1 Z n=1 (4-3)² not is given by - √/24 x = = =…

A: Using ratio test, to find wheather series is convergent or divergent in which interval.

Q: Ju udv = Uv -Ivdu to Explain why the substitutions below are inappropriate. Let du: = x dx 1.…

A: We can explain why the substitution is inappropriate in the following steps.

Q: Example 99 Consider the set M = {(x, y) = R²: x,y #0}. Find M. Solution:

A: The orthogonal complement are subspace

Q: 1. f(3x + 1)¹5 dx 2. f(8x³ + 2x² - 1)7 (6x² + x) dx x-2 3. f dx √50-5x3

A: LetI=∫(3x+1)15dx put  u=3x+1differentiate du=3dxdu3=dxThereforeI=∫u15du3Take constant…