Let r = (2-8, e4-61, (t + 1)−6). Compute the derivative. (Use symbolic notation and fractions where needed. Give your answer in the form (x(t), y(t), z(t)).) dr dt Incorrect = (2e²1,-6e4-61-6(1+1)-7) ,-бе

Q: dy 7. a) Prove that, So √at-yt [ro] 4a√2π

A:

Q: Find the first partial derivatives of the function. f(x, y) = -5xy

A: given function is

Q: Simplify the trigonometric expression below by writing the simplified form in terms of sin z.…

A:

Q: The area of a circle, A, in terms of its radius, r, is given by A(r) = r². The radius in terms of…

A:

Q: ) An object is pulled with a 5 N force at an angle of 30° to the horizontal. Find the horizontal and…

A:

Q: 7. For what values of r does the function y = y" + 6y' + 8y = 0 ? erx satisfy the differential…

A:

Q: Given f(x, y) =-3x¹ – 2xy² – 6y5, find - - fz(x, y) = fy(x, y) =

A:

Q: Show that dri dt = r2 dr2 r₁ dt. If r₁(t) = t², what is when A₁ = 4A₂? dr2 dt

A:

Q: 1. Determine vector and parametric equations for the line with z-intercept 4 and is parallel to the…

A: To determine the vector and parametric equations for the line with -intercept 4 and is parallel to…

Q: Find the slope of the curve y = cos The slope of the curve is (Type an exact answer.) ¹x at √3 T 2'6…

A:

Q: Differentiate but leave your answers in unsimplified form. a) y = 5x³ 4x-² +6 c) y = √x² + 3x b) y =…

A: We know that the derivative of x^n=nx^(n-1)

Q: Let f(x) = In(x) and g(x) = log2x. For all 0 g(x) O True O False

A:

Q: Evaluate the line integral Jc (2x³y³) dx + (9x³ + y³) dy where C is the unit circle, and verify…

A:

Q: Apply the midpoint and trapezoid rule to the following integral. Calculate the approximations and…

A: Let's solve the integral using midpoint method.So we divide interval [1,5] into 8 subinterval of…

Q: Let f(x, y) = 125-3x²-2y2² Evaluate f(0, 3)

A: f(x,y)=sqrt(125-3x2-2y2)Find f(0,3)

Q: To test the series Test, as is the case with all series of this type.) According to the P-test: 1…

A:

Q: Evaluate the derivative (t'r(t)), where r(t) = (t¹0, t², t). (Use symbolic notation and fractions…

A:

Q: Using the substitution u = 1+x^2, convert the integral into one involving only the variable u. You…

A:

Q: The base of a three-dimensional figure is bound by the line = 2 cos(y) on the [ - 12/17, Vertical…

A:

Q: For the functions w = 2x² + 3y², x= cost, and y = sint, express terms of t and differentiating…

A:

Q: 6. The tension in a rope that is being used to drag an object with a mass 100 kg across the floor is…

A:

Q: 1. Simplify first, then evaluate. Do not use calculator. a) logg 6-logg 3 +logs 2 b) log, 3√3

A:

Q: j(x) = x=5 X X 9. j(5) = j(x) 10. lim j(x) as x->5 = 11. j(0) = 12. lim j(x) as x->0 from the left =…

A:

Q: Determine the equation for the tangent to the curve f(x)=In(1+e') when the tangent is parallel to…

A: Here, we need to determine the equation for the tangent to the curve f(x) = ln(1+e^x) when the…

Q: O с 5. Given the function below, what would be the domain of the function's inverse? 1/2 -0.5 ≤x≤0.5…

A: Domain of a function f(x) is defined as the set of valued of x for which the function gives a…

Q: Determine the interval(s) on which the function is (a) increasing, (b) decreasing, and (c) constant.…

A: Graph is given.

Q: Evaluate the volume of the cylinder whose top is the part of hemisphere z = √2 x² - y² in the first…

A: We have to find the volume of the cylinder.

Q: At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

A: Note:- As per our guidelines, we are supposed to answer only one question with a maximum of three…

Q: 1. Differentiate. a) f(x) = x43x b) g(x) = x² — e√x -

A: We need to perform differentiation.

Q: Suppose an airplane is flying 170 mph with a heading 25° east of south (295° measured…

A:

Q: A local business has a Cost function given by of students enrolled. Find the average rate of change…

A: The average rate of change of a function f(x) from x=a to x=b is

Q: 7. a) Prove that, fo-y²= 4√2n a dy = [163/²

A: Note:-Since you asked multiple questions , according to our policy we can solve only first question…

Q: e or plane that is perpendicular to the planes 4x-2y + 2z= -1 and

A:

Q: Given the initial condition y(0) = 2, find the particular solution of the equation e'y' - 2x = 0

A:

Q: q 22. 16 determine the magnitude and direction of the vector v = and also show that  v = |v|u ,…

A:

Q: f(x, y) = √5x² + 3y² fz(5,-2) =

A:

Q: 9-14 Use the method of cylindrical shells to find the volume generated by rotating the region…

A:

Q: Calculate the derivativer(g(t)) using the Chain Rule. r(t) = (e.e.3) g(t) = 8t +6 (Use symbolic…

A:

Q: 5. Which equation can be solved by referencing the graph below? -1/2 -11/4 3 cosx – 1 = sinx O…

A: The range of both cosine and sine function is .The value of the sine function is zero for all…

Q: Given the function f and the point Q, find all points P on the graph of f such that the line tangent…

A: The equation of the line passing through the point (a,b) and slope m is given byy - b = m ( x - a)

Q: Find the gradient of the function f(x,y)=√2x+3y at the point (-1,2). Then sketch the gradient…

A:

Q: Find the limits. (a) lim -t 10 t-x 5 + e-t (b) lim 1-2et t-∞ 1 + 3et (c) lim

A:

Q: Q5. The attractive force between 2 oxygen atoms is given by the equation F = k(ex-6e-2x), where x is…

A:

Q: Solve the equation below algebraically. Support your answer(s) by including the solution graphically…

A: The range of cosine function is .The period of cosine function is .

Q: Let D be the triangle in the xy plane with vertices at (-2, 1), (1, 0), and (3, 4). Describe the…

A:

Q: O Country A had a GDP per capita of $10000 and Country B had a GDP of 1000 in 1960. Country A has…

A:

Q: Let R(x, y) = 0.7x³y² -5x³ +6y², find the second partial derivatives: a²R oy²

A:

Q: enter , type P o e field below accepts a list of numbers or formulas separated by semicolons (e.g.…

A:

Q: 5. Find the absolute maximum of f(x) = x¹e-77 on [0,4]

A: The given function is,

Q: 7. Identify if the statement is Always True, Sometimes True or Never True. If lim f(x) exists, then…

A: