1. Find the area bounded by the parabola y?=4ax, the x-axis, and the lines x=4a, x=9a. 2. Find the Area bounded by the curve y=4-x2 and the x-axis. 3. Find the area of one of the sine curve.

Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

A:

Q: teimx dx xF I+ x²

A: Given query is to find the integral.

Q: Question 6 of 17 Find an equation of the parabola with vertex (1, 4) and directrix x=-3.

A: Given that vertex of parabola (1,4) and directrix x=-3  To find the question of parabola  Again…

Q: Differentiate the following functions. Simplify and factor your answer where possible. a) f(x) = e2x…

A:

Q: Given a = 3 units, = 1 unit and the angle between a and b is 30°, determine o) the exact value of (…

A: Solution:

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. In(5x) dx u…

A: We will evaluate the given integral as shown below

Q: For the function f(x) ex x>0 a) Determine the coordinates of all critical points. b) Use the first…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Given

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: This question can be solved using the concept of tangent and normal in vector form.

Q: 25. The graph of y = a* +b is shown below. Find the EXACT values of a and b. 6- (2,5) 4- 2- y = a*…

A: This question is based on substitution of points.

Q: Find the area of the enclosed region bounded by the graphs of y=e^x, y=x, the y-axis and the line…

A: Here we have to find the area of the enclosed region bounded by the graphs of y=ex,y=x,the y-axis…

Q: esing pyphagoras th, Diff wt to t 2xda +rydy 20 at da dt az3 m

A: Apologies for the inconvenience.   Let, x = the distance from the wall. y = the height of the top of…

Q: The plot below represents the function f(x): 5- 4 2 -5 -4 -3 -2 -1 I 2 3 4 5 -1 -2 -3 -4 Evaluate f(…

A: Consider the function

Q: furt A)APproximate tue area unde hex)=X2 from x=0 to X=2u5ing four rectungles and X=0 a left and…

A:

Q: answer is partialy Answer the questions for the following polar equation. 3 r = 1- cose (a) Identify…

A: Parabola

Q: Find the arc length Lof the graph of r(t). r(1) = r° i+t j+Võr² k, 3 <155 V61² k, 3 <1< 5

A:

Q: A particle is moving in a straight line according to the position function s(t) = t° – 6t2 +9t + 5,…

A:

Q: Convert x = 6 to an equation in polar coordinates in terms of r and 0. (Use symbolic notation and…

A: Given: x=6

Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

A: Given :

Q: Describe the graph of the equation: r = 7hi – 9j + (1 + 61)k. [Choose the correct answer.] O The…

A: Given problem:- Describe the graph of the equation: r = 7ti − 9j + (1 + 6t)k.

Q: Verify Green's Theorem by evaluating both integrals y? dx + x² dy Ne dA ду ax for the given path. C:…

A:

Q: 5) FIND THE MACLAURIN MALLAL fOR SERIES fa)=x cos (2x) %3D

A:

Q: Problem:

A: answer is in next step

Q: Solve the following differential equations of 1 x’y" – 2xy' – 4y =

A: To find the solution of given differential equation.

Q: For the function f (x) = xe¬*: a) Determine the coordinates of the critical point. Use exact values.…

A:

Q: Find div F and curl F if F(x, y, z) = 11y°z'i – 14.x°z°j – 7xy*k. | div F= curl F=

A: Given problem:- Find div F and curl F if F(x, y, z) = 11y5 z7 i - 14x6 z8 j – 7xy4 k.

Q: y = sec?(x), 0s

A: Here is the solution

Q: I can't understant the solution :<

A: Let, radius = r Height = h When r = 8, then h = 22. Using this we get a relation between r and h.…

Q: The widths (in meters) of a kidney-shaped swimming pool were measured at 3-meter intervals as…

A:

Q: You record the temperature every hour from midnight until 8:00a.m. You see that the temperatures (in…

A:

Q: Find an equation for the hyperbola that satisfies the given conditions Foci: (+5, 0), vertices: (±3,…

A: Given (5,0)=(h+c,k)    hence k = 0(-5,0)=(h-c,k)h+c=5h-c=-52h=0h=0Therefore (h,k)=(0,0)

Q: Evaluate the integral. yz dx dz dy O8 68 3.

A: We have to evaluate the given integral

Q: Find the arc length L of the graph of r(t). r() = r° i + 1 j+Vor k, 3 <t<7 L = i

A: Given problem:-

Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

Q: 5 y = 4x+3y+2 3r+2y+1

A:

Q: EVALUATE. 2022 a) x n (xl dx dx 2x+3x+7 dx (x+1) (x² +S)

A: This question can be solved by applying the concepts of indefinite integrals.

Q: The surface area of a spherical snowball is increasing at a rate of 9 mm2/min. Find how fast the…

A:

Q: Sol V= cotcex) dx /2

A:

Q: 2n Graph the sets of points whose polar coordinates satisfy the inequalities Osrs1. Choose the…

A:

Q: Determine whether the following series are absolutely canvergen t, Conditionally convergent,…

A:

Q: -z“, where T is The temperature at a point (x, y, z) is given by T(x,y, z) = 200e measured in…

A:

Q: Find the derivative of y sinh-(13x). (Use symbolic notation and fractions where needed.)

A:

Q: The graph of f shown below has vertical asymptotes at X= - 2 and x = 4. Find the following limits.…

A: Solution is given below

Q: Find the general solution of the given second-order differential equation. 5y'' + y = 0 y(x) =

A: If the roots of the auxiliary equation is complex i.e, α±iβ , then complete solution is…

Q: 291 pind the lengty of tue cerve over the ginernineval a) 1o ) so 20 e) 40 d)s 11/12

A:

Q: 5y'' + y = 0 y(x) =

A: Consider the differential equation  5y''+y=0

Q: sin' (12x) dx =

A: TO find : ∫sin3(12x)dx=?

Q: 8. Describe the type of indeterminate form. Evaluate the limit using L'Hôpital's Rule if necessary.…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…