Compute u v if u and v are unit vectors and the angle between them is R|4

Q: P 3. Evaluate the integral fx cos(3x²) dx as an infinite series. (You do not need to find the radius…

A:

Q: A rectangular base box must be constructed, with a sheet of cardboard 40 cm wide and 50 cm long,…

A:

Q: Evaluate the integral. Select the correct answer. 2√ 213, 9 S -1 -1 tan 2 ( 1² + 2x + 4) - ²¹ (+²) -…

A:

Q: Express the integral in terms of the variable u, but do not evaluate it. So e15x-14 dx; u 15x - 14…

A: ∫01e15x-14dxLet u=15x-14.=∫-141eu115du=115·∫-141eudu=115eu-141=115e-1e14=e15-115e14

Q: It f(x) = x² - 4x - 3, find f (x + 3). 10. If g(x) = 2x³ + 4x − 5, find g(x − m)

A: 9) The given function is: f(x)=x2-4x-3

Q: 4. What is the length of the latus rectum of the ellipse whose equation is + = 1. 16 25

A: Latus rectum of an ellipse is a straight line passing through the foci of the ellipse and…

Q: Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your…

A: We need to find parametric equation.

Q: 1.4 Assuming that C₁ Cos (wot) and C₂ Sin (wot) in 1.2 are two independent solutions of the SHO…

A: It is given that C1 Cos( W0t) and C2 Sin(W0t) are two independent solution of the SHO differential…

Q: 12. For an object whose velocity in ft/sec is given by v(t) = cos(t), what is its distance, in feet,…

A: Topic = Integration

Q: The resistance R of a copper wire at temperature T = 25 °C is R = 18 22. Estimate the resistance at…

A: Let's solve.

Q: B)Solve the differential equation =(3+x¹)+x²e³x.

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

A:

Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t2k,   u(t) = 5ti +…

A:

Q: Write a polynomial f(x) that meets the given conditions. Answers may vary. Degree 3 polynomial with…

A:

Q: Let g(x, y, z) = xy + yz + zx. Find a nonzero vector perpendicular to the level surface g(x, y, z) =…

A:

Q: Step 2 Apply the rule of integration by parts. J u dv = uv - Submit J Let dv = ew dw and integrate…

A: topic- indefinite integral

Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given: y'+ye3x+7=-2y2

Q: nd the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2 You…

A: Given :limx→21-x21-x2

Q: 3. 31 √ √(²x- (2x - 4y)dydx 1 -1

A:

Q: Is the function has a extreme point? If yes, Locate the extreme point: 1 + 3x V4+5x2 y

A: Find derivative of function and equate to zero to find critical points

Q: As per the trigonometric substitution x = sin(0), the following triangle is obtained. cos(0) Submit…

A:

Q: Consider the following situation, which involves two options. Determine which option is less…

A: To find out which one is less expensive.

Q: 38. A rectangle is inscribed in a semicircle with diameter 10 centimeters as shown. Express the area…

A:

Q: - 1. 1 [(ow + √w) dw

A:

Q: Find the arc length of the graph of the function over the given interval. y = In x, [1, 8] Step 1…

A: topic- arc length of a curve

Q: 4. 4 1 [x²ydxdy 20

A: The objective of the question is evaluate the double definite integral.

Q: (b) (c) 0 (69) (89-19) 0 0 0 0 0 0 1 2 3 (9) (6 9.6 9.6 2 1 0 0 0 1 0 4. Determine whether the…

A:

Q: f(a+h)-f(a) h a. Use the definition mtan = lim h→0 b. Determine an equation of the tangent line at…

A:

Q: (C) (In Mpg) for a certain vehicle can be approximated by m (x) = -0.03x +2.645x-35.029, where x is…

A:

Q: Use logarithmic differentiation to find the derivative of the function f(x) = (sin 7x)/x c) Coal is…

A:

Q: 9x¹+x x-100 2x¹45x²-x+6 iv. lim

A: Given limx→∞ 9x4+x2x4+5x2-x+6

Q: You could take a 15-week, three-credit college course, which requires 10 hours per week of your time…

A: Given :  3 credit college course for 15 weeks. Which requires 10 hours per week

Q: Starting with the graph of write the equation of the graph that results from reflecting about the…

A: Reflection

Q: Complete the table, for the following investments, which shows the performance (interest and…

A:

Q: 8. [ V4 – x? xdx

A: The given integral is: I=∫4-x2xdx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: 31-4 A piecewise function f(x) is defined by f(x)=x²+3x+4 x² -7x+12 Part A: Graph the piecewise…

A:

Q: Suppose the speed of a car approaching a stop sign is given by v(t)=(t−13)2​, for 0≤t≤13​, where t…

A: The given data is: vt=t-132, for 0≤t≤13 (a) Find v'7

Q: Solve the following initial value problem. Provide your answer below: f(x) = ƒ"(x) = 36x² + 6x – 10,…

A:

Q: 2. Find the equation of the line tangent to the circle x² + y² + 6x - 2y - 15 = 0 at the point…

A: Here the given circle is , x2+y2+6x-2y-15=0 We need to find the tangent to this circle at the point…

Q: Find normal line and parallel plane to the function f(x, y, z)=√xyz - 4 At point (1,2,8).

A:

Q: The combined electrical resistance R of two resistors R₁ and R₂, connected in parallel, is given by…

A: To find the rate of charging.

Q: Solve using variation of parameters: y" - 2y + y = e¹/(1+1²) + 3et p= ₁ ² + ₂ tet (Use 2 decimal…

A:

Q: 3) Consider the autonomous DE: y' = y² + 3y - 10 A) Find the critical points of the given DE.

A:

Q: ) Find the volume of the solid whose base is the region in the first quadrant bounded by y = x5, y =…

A: Here, the cross-sections perpendicular to the x-axis are semicircles whose base span from y=x5 &…

Q: 13. Sketch a graph of a rational function that satisfies the following conditions f(0) = 0, f(-4) =…

A:

Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

A:

Q: Example Two tanks T₁ and T₂ each contain 100 gal of water each. In T₁ the water is pure, whereas 150…

A: AS WE KNOW THE GENERAL FORMULA IS dy1dt=inflowminconcentration of…

Q: Determine if the graph can represent a polynomial function. If so, assume that the end behavior and…

A: Solution

Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

A:

Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.