Find the area of the shaded region. x = y² - 4 -2 y 3 -3 y = 1 x = e² 2 y = -1 4 X

Q: 2. Show that the function f(x) = xsinx has in infinite number of Critical Points by doing the…

A: The given function is : f(x)=xsinx Now finding the derivative f'(x) :

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: Given the two complex numbers: 2₁ = 2 + 4i and Z₂ = √5 -3i 1) Find the value of the complex number…

A:

Q: G] Example: Raggs, Ltd., a clothing firm, has fixed costs of $10,000 a year. These costs, such as…

A: The total cost Cx in dollars of producing x suits a year is given by a function C.Cx=Variable…

Q: Obtain general solution xcos2ydx+tanydy=0

A:

Q: A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000. The…

A:

Q: Find the differential equation by eliminating the arbitrary constant/s. y = = Aex cos x + Bex sin.x…

A: We differentiate the number times as the number of arbitrary constants present in the equation and…

Q: C) g'(x) = 3x²; g'(1) = 3 D) g'(x) = 3x2 + 5; g'(1) = 8 mits to find the derivative function f' for…

A:

Q: √t 12. If a factory continuously dumps pollutants into a river at the rate of tons per day, then the…

A:

Q: Suppose that a volcano is erupting. Readings of the rate r(t) at which solid mate- rials are spewed…

A: Given data   t 0 1 2 3 4 5 6 r(t) 2 10 24 36 46 54 60

Q: Express the following functions in the form u+iv • f(z) = \n (1+z) P

A: Given function is: f(z)=ln(1+z) Let z=x+iy

Q: 9. The function f is continuous on the interval [3, 11] with some of its values given in the table…

A: Let's find average rate of change.

Q: In problems 16-19, each limit represents the derivative of some function f at some number a. State f…

A: This question can be solved using the concept of derivative of a function y=f(x) at a given point…

Q: 2. If f (x - 2) = 2x + 5, what is the value of each of the following?

A:

Q: Find the area of the region enclosed by the curves y = 2 - x² and y = x. (a) (c) 9 2 54 (b) (d) 40 7…

A:

Q: Prove that tan'z= leto 1/2 in (1+2) tan't z • tanw=Z Z = Sinw cosw

A:

Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: (a) Find the Taylor series expansion of the function et around x = 0 (b) Use the series above to…

A:

Q: Assume that is an acute angle. If sec8=6, find the exact value of sin 8. Write your answer as an…

A:

Q: 3) f(x) = 2x² + 4x Find a) f(3) b) f(x - 1) c) f(a+h)-f(a)

A:

Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

A:

Q: sing the substitution u = √x + 3, evaluate 2 S. VELVE √(√x + 3)2 dr.

A:

Q: First rationalize the numerator, then find the limit. Enter the exact answer. If the limit does not…

A:

Q: Rule

A:

Q: the derivative. 28) y = x5/6 A) 5x7/6 B)x1/5 a C)/x-5/6 D) Ex-1/6

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: A sphere has the equation  x^2 +4x + y^2 -6y +z^2=3 what is the center of the sphere please give…

A:

Q: I could write on paper

A: Volume of the parallelopiped , V =xyz

Q: Given x and f(x), fill out the rest of the table. X -2 -1 f(x) f(x) - 1-6 f(x - 1)-7 -f(x) 5 f(-x)…

A:

Q: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -

A:

Q: 10. Use the squeeze theorem to find lim f(x) if 2x+2 ≤ f(x) ≤ x² +3. x-1

A: Given: Use the squeeze theorem to find limx→1f(x) if 2x+2≤f(x)≤x2+3

Q: Use Green's Theorem to evaluate 90 O O -384 O -48 fayd r²y² dr + (yr³+ y²) dy where C' is shown…

A: As we know from Green's theorem: ∫cMdx+Ndy=∫∫R∂N∂x-∂M∂ydA Where, ∬dA=∬dxdy or ∬dydx And We know the…

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: Use the given conditions to write an equation in point slope form and slope intercept form. 8. Slope…

A:

Q: Find the integral. (Use C for the constant of integration.) t (294 - t2)3/2 dt

A:

Q: Given the graph of f(x) = x² as shown, graph the function - 5ƒ(x + 4). 10+ 9+ 8+ 7+ 6+ 5- 4+ 3+ 2+…

A: The function is fx = x2 The graph of the function is To evaluate: The graph of the function -5fx+4

Q: Consider 3 4+2³ (a) First, define this as a Mathematica expression and compute the third derivative.…

A:

Q: question 21. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

A: We will find the required.

Q: Find the value of c such that the function is continuous on the entire real number line. f(x)=…

A: Topic = Functions

Q: Find the solution of the differential equation (6x² − y + 3) dr+ (3y² - x - 2) dy=0 1 O x + O 2x³ O…

A:

Q: What about the graph, where to plot the both lines ???

A: As S denotes the number of bowls of salad and P denotes the number of pizza slices .Also given that…

Q: Use the given conditions to write an equation in point slope form and slope intercept form. 7. Slope…

A: Here we need to find the equation of line. The solution of given problem is as follows.

Q: 1. The graph of f "(x) is continuous and decreasing with an x-intercept at x = -3. Which of the…

A:

Q: Make a table of values for the equation. x + y² = 9 X Sketch a graph of the equation. у -2 -1 0 1 2

A: Substitute y=-2 in x+y2=9 and calculate the value of x.       x+y2=9x+-22=9       x+4=9…

Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

A: To verify that the solution of the DE d2xdt2+k2x=0 is x=sinkt.

Q: Find the value of a, b, c, and d. Enter all answers in exact, reduced form. No decimals are allowed.…

A: Please refer to the image below

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

A:

Q: A sports franchise revenue can be modeled by the function R(t) = 337 + 8t. Their operating costs are…

A: Given data:- Revenue function R(t) = 337+8t Cost function C(t) = 245+20t

Q: 2. The population of a city is growing continuously by the same percent each year. The population at…

A: We can solve this by following methods.

Q: Find the differential equation for the given family . y ^ 2 = C * x ^ 4 - 2

A: The given  equation is; y2=Cx4-2.

Q: 13. Recall that nonzero vectors u and are called collinear if there exists = a nonzero scalar a such…

A: Given data:- Nonzero vectors are u→ & v→ Nonzero scalar α v→=αu→