DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

Q: Evaluate (2x + 3√/Y) ds where C is given in the accompanying figure. (2x+3√/Y) ds- (Tyne an exact…

A: ds = dxdt2+dydt2 dt

Q: 6. csch x dx

A: To find the integral of the given function.

Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

Q: fesch² (1- csch² (1+ 3x) dx

A: Hyperbolic function need to be integrated.

Q: Using the Ring or Washer method, what will be the equation of the volume of the solid formed when…

A:

Q: Find the volume of the parallelepiped determined by vectors , and

A: Find the volume of the parallelepiped determined by vectors <3,1,4>, <2,0,2> and…

Q: I. Directions: Determine if the function is continuous on the given interval 1-3. f(x) 2 12-x² ; [1,…

A: 1. fx=212-x2; 1,32. fx=2-x+3; -3,-13. fx=1if x≤2x2-3if x>2; 2,4

Q: 2 = 2(0)+7(0) + ²₂ D 6. Use a(t)=-32 feet per second squared as the acceleration due to gravity. A…

A:

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: 5. sech 2x tanh 2x dx sech

A:

Q: Evaluate the integral cosx dx from í/3 to π/2 * 0.134 0.500 0.293 0.707

A:

Q: (a) Find the vertices, foci, and asymptotes of the hyperbola. (Enter your asymptotes as a…

A:

Q: Use the linear approximation to estimate In (√0.99).

A:

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±7), vertices: (0,…

A: We have to solve above hypobola question

Q: Q2): For each of the following functions,determine if f(x) is convex, concave, or none of these.…

A:

Q: nd price (demand) functions C(q) = 100q+43,700 and p(q) = 2q + 890, what is the marginal revenue at…

A: Please refer to the image below

Q: The function f(x) = 900 represents the rate of flow of money in dollars per year. Assume a 10-year…

A:

Q: Given that -3 9+x² following functions: (-1)n+1 32n+1 4x (9+x²)² Σn=0 2. g(x) = x2n. Obtain the…

A:

Q: If f(x)=5x(sinx+cosx), find f′(x) =

A: Product Rule of differentiation : du.vdx=u.dvdx +dudx.v dxndx=n.xn-1 dsin(x)dx=cos(x)  and…

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 and y = 2x…

A:

Q: You deposit $2000 in an account with 4% annual compound interest. Complete the following, assuming…

A:

Q: Questions 1-4: The graph of a function y = f(x) on the interval [-3, ∞) is shown below. Use the…

A: Given.

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

A:

Q: Derive implicitly—Implicit differentiation. Please show a detailed solution. Also, comprehensive and…

A: In this question, we want to differentiate the given expression implicitly.

Q: The function defined by y=√√²-x²2 has as its graph a semicircle of radius r with center at (0,0) (as…

A: The given equation of the semi circle: y=49-x2.We need to find the volume when the semi circle is…

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

A:

Q: Approximate the area beneath y = sin x on the interval [o, π] using the Trapezoidal Rule with n = 4…

A:

Q: The solution of the differential equation y' + 2xy = Ky when y(1)= K is

A:

Q: What is the exact value of sin(255°) +sin(195°)? Show your work for full credit.

A:

Q: 2)dy - ydx = 0 (x + y cot ) dy

A:

Q: = ²/²/² ( e ² + e^²^²) 3. Obtain the Maclaurin series for cosh x using the fact that cosh x =

A: Given the function,   cosh x=12ex+e-x

Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Explained below

Q: What is the y-coordinate of the centroid of the plane region bounded by y = x^3 and y=x^2? O 2/5 3/5…

A: We can solve this as follows:

Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

A:

Q: II. Directions: Find the slope of the line tangent to the given curve at the indicated point 10-12.…

A:

Q: A company produces computers. The demand equation for this computer is given by p(q) = -5q+6000. the…

A: Given the demand functionp(q)=-5q+6000where q represents the number of units:total Revenue…

Q: The joint cost (in dollars) for two products is given by C(x, y) = 24 + x² + 3y + 2xy where x…

A:

Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

A:

Q: ular bird sanctuary with one side along a straight river is to be constructed so that it contains 72…

A: Please refer to the image below

Q: Derive the standard equation of a circle if its general equation is x² + y² - 10x - 6y + 14 = 0.…

A:

Q: 1. f³₂ (x² − 3) dx -2

A: Given :∫-23x2-3dx

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 6x2 + 6y2, where x…

A:

Q: 1. Evaluate L²S³ (2y³ + x²y) dx dy

A:

Q: As part of a chemical experiment, a scientist determines that the number sodium in a chemical…

A:

Q: 1) If y = (x-a)√2ax-x² + a² sin-¹(*), then y' = 2√/2ax - x² a a is constant. 2) If f(k)= k√a²-k² +…

A:

Q: Using the Law of Sines to find a triangle with one obtuse angle if ZA = 50°, a= 23, b = 25. If no…

A:

Q: An 84 cm wire is cut into three pieces. The second piece is 4 cm longer than the first piece and the…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.8q +800, what profit can be…

A:

Q: Use the linear approximation to estimate In (√0.99).

A: Given problem:- Use the linear approximation to estimate In(3√0.99).

Q: C. Find the slope and the equation of the tangent line to the curve. 23. y 2x−x+2 at (-1,5) 24.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…