Find the vector equation of the plane that contains the parallel lines [x, y, z]= [0,1,3] + [-6, -3,6] and [x, y, z]=[-4,5,-4]+s[4,2,−4] .

Q: 2n+25n²+32n-15 The nth term of a sequence is represented by 6n²+2n³-11n²-2n+17 What is the limit of…

A:

Q: X Find the derivative of y = x • xx−1 X. x ln(x) x* (ln(x) + 1) In(x) + 1

A:

Q: The matrix on the right results after performing a single row operation on the matrix on the left.…

A: In the given matrices R2 and R3 are same. We have to perform row operation to change row R1 only.

Q: Find an equation for the line tangent to the curve y = (√x - 9)(x³. 6) at x = 1.

A:

Q: Let f(x) = 11x³ over the interval 0 ≤ x ≤ 1. Set up the integral for the surface area generated by…

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

Q: 5. Let f(x) = [2-kx k+x with the value of f(1) to be determined. (a) Compute lim f(x) in terms of k.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Using the method of "First Principles" and showing all steps, determine the 4 derivative of the…

A:

Q: you know that a sphere has the equation of  x^2 + y^2 +z^2 -6x +4z =3 are the following points…

A: The equation of sphere is:-Now add 9 and 4 both side:-

Q: The population of a slowly growing bacterial colony after t hours is given by p(t) = 3t² + 21t +…

A:

Q: 1. when the a value is a fraction between 0 and 1, then the graph is compressed true or false 2.…

A:

Q: V9-4x2 x2 dx

A: Here we have to evaluate the integral,.

Q: Assume that x and y are both differentiable functions of t and are related by the equation ㅠ dy Find…

A:

Q: Use the disk method to find the volume of the solid of revolution bounded by the x-axis and the…

A: Region bounded by x-axis and Using Disk method , Volume of solid of revolution about x-axis will be

Q: Find the maximum value of ƒ(x, y) = x¹y³ for x, y ≥ 0 on the unit circle. fmax =

A:

Q: State the range for the function f(x) = -e* + 2:

A: Find range and choose the correct option

Q: 25. Determine the value of k so that f(x) is continuous. Show work. x² - k f(x) = 2x² + 7x - 22 x≤2…

A: given function is

Q: if both f (x) and g (x) are differentiable, then d d [ƒ(x). 9(x)] = f'(x). g' (x). O True O False

A: given both f(x) and g(x) are differentiable.

Q: 5. Let G(x) = = = f* tan-¹(s) ds x2 Find G'(x)

A: Fundamental theorem of calculus

Q: Evaluate the integral -2 Te ex dx Note: Use an upper-case "C" for the constant of integration.

A:

Q: Assume that F(x,y,z(x,y)) = 0 implicitly defines z as a differentiable function of x and y. The…

A: Assume that  implicitly define  as a differentiable function of  and .The partial derivatives of…

Q: Suppose that f(2)=-4, g(2) = 3, f'(2) = -1, and g'(2) = 5. Find h'(2). (a) h(x) = 3f(x) 2g(x) h'(2)…

A: Given that  and .To find the derivative value of .Derivative formula:

Q: Find three positive numbers whose sum is 120 and whose product is a maximum. (Enter your answers as…

A:

Q: Consider the following integral. Sketch its region of integration in the xy-plane. (a) Which graph…

A:

Q: Find the slope of the line tangent to the curve e at point (0, 0) - sin(x + 5y)

A:

Q: dx [(x - gx)] dar [21/a>

A: To differentiate the following functions.(i) (ii)

Q: 1. у ул y=3x - x² 0 y=x (2, 2) AX

A:

Q: Consider the following. f(x, y, z) = x²yz - xyz³, P(2, -1, 1), u = (0, -—-. (a) Find the gradient of…

A:

Q: Evaluate the integral. 2 0 X-2 -dx 2 x - 4x + 5 12-20 X-2 dx≈ x² - 4x + 5 0 (Type an integer or…

A:

Q: 11. Consider the plane and the line with these equations 0 = x - y - 2z + 10 a) : a must b) Find all…

A:

Q: 2x Find the derivative of Y = e²ª sin¯¹(x) + ln(x) y

A: y=e2xsin-1x + ln(x)Find the derivative of the given function.

Q: Suppose 3x² + 4x + xy = 3 and y(3) = = y'(3) = -12. Find:

A:

Q: Consider the curve y = x² + 3x +5. Find the slope of the secant line at the point where x = 9. Oh +0…

A:

Q: the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: We have to integrate the given function.

Q: e (25x) lim e x→2+

A: Limx-2+ e(5/(2-x))

Q: 27. S cos5 x sin³ x dx

A:

Q: Let Q(t) denote the population of a certain country at time t. In 1970, the population was 2.5…

A: The first situation is represented as, (where growth factor=1.018 and growth factor=1+r, here r is…

Q: Evaluate the following indefinite integral. 1-3 Do not include the constant "+C" in your answer.…

A:

Q: 25. Determine the value of k so that f(x) is continuous. Show work. x² - k 2x² + 7x-22 x≤2 x>2 x-2…

A: A function f(x) is said to be continuous at a point a, if Left hand limit and right hand limit and…

Q: Examine the function for relative extrema and saddle points f(x, y) = x³ 3xy + y³

A:

Q: What is the rectangular form of the polar equation r = 4sin(0)? Choices: x = 4sin(0), y = 0 x = 0, y…

A:

Q: 4x³-13x²+3x+2 x²-4x+3 dx

A: I=

Q: Find the first partial derivatives of the following function. h(x,y,z) = cos (7x+3y+z)

A:

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: What is the component form of the vector represented by 6a when a = (-2, 3)? 6a =

A:

Q: Find the four second partial derivatives of the following function. 5x z = 8ye

A:

Q: Express the function G in the form fo g. (There is more than one correct answer. The function is of…

A:

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: Find all the second partial derivatives. sin(3s² - 4t²) V =

A:

Q: Evaluate the integral. 6² tep 1 30 6x² + 7x + 1 [² The integrand of x6x² + dx 30 6x² + 7x + 1 x7 x +…

A:

Q: A solid of revolution is generated by rotating the region between the x-axis and the graphs of f(x)…

A: