The distance from the point K(3, -2, 0) to the az- plane is Select one: O-2 O √13 O 0 02 O None of them

Q: Let C be the curve y = 12 11 10 9 8 7 16 16 5 A m Cy 1.5 x³ 1 + for 0.6 3.7. 3x 4 2,5 3 Find the arc…

A: We are given a curve C : y= x3/4 + 1/(3x)  for 0.6≤x≤3.7. We have to find arc length of C.…

Q: = / y ²³. (X²+1) (3x+4) 5/ (2x-3)(x²-4) Find dy da

A: To find dydx:

Q: Geometric Interpretations of Equations In Exercises 1-16, give a geometric description of the set of…

A:

Q: Evaluate the following integral or state that it diverges. S (15 In x)dx Select the correct choice…

A:

Q: Given g(x) = 9x + 5x, answer the following: Part: 0/3 Part 1 of 3 (a) Find g (-x). g (-x) = 0⁰ 0101

A: A function g(x) is even if g(-x)=g(x). A function g(x) is odd if g(-x)=-g(x).

Q: f(t) = sin(wt) u(t) Do the laplace transformation of the math in details.

A: we have F(t) =sin(ωt) u(t)

Q: Which of the following is a unit vector parallel to the vector ? Select one: 2 0 8 1 4 <- 81¹ 81¹…

A: Let's solve.

Q: At what point do the curves r₁(t) = (t, 5 − t, 35 + t²) and r₂(s) = (7 — s, s − 2, s²) intersect?…

A:

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0, 4, — 3), and R= (-6, -1, - 5)

A:

Q: For the function graphed below, find the values of x at which the derivative does not exist. (Enter…

A: Solution : Given that the figure is

Q: find the tangent line of the function below f(x)=x+4/x and (2,4)

A: This question is based on finding slope to find out tangent line at a point.

Q: * The differential equation 2ydx-(3y-2x)dy=0 is Exact homogenous and linear Exact and linear but not…

A: The answer is given below:

Q: Use any of the results in this section to evaluate the given integral along the indicated closed…

A: Cauchy’s Integral Theorem : If f(z) is an analytic function in a simply-connected region R, then…

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: A tank contains 240 litres of fluid in which 50 grams of salt is dissolved.pure water is pumped into…

Q: The Taylor series for f(x) = x³ at 4 is Σ cn(x − 4)". n=0 Find the first few coefficients. CO C1 =…

A:

Q: y = f(x) = 8x² - 4x + 5 (a) Find the differential of f. dy = (b) Use your result from part (a) to…

A: Follow the procedure given below.

Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y…

A:

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: We have to analyze and sketch a graph of the function and find any intercepts, relative extrema,…

Q: If 4x² - y² = 64, show that ds² = 1/2 (15x² (5x² - 16) dx².

A:

Q: 0. Given the following functions, make a sign sign diagram for • the first and second derivative and…

A:

Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

A: We can find the area of the bounded by the given curves.

Q: The intervals on which f(x) = x² ln x is increasing and decreasing, and the intervals of concavity…

A:

Q: The Maclaurin series of the function f(x) = 6x²e-4² can be written as f(1) = Σ₂² n=0 where the first…

A:

Q: Evaluate 2 1.³ sin(2x + 3)dx -0.9989 None of them -0.9998 1.21 0.9989 -0.9899 0.9899

A: ∫0π/2 sin(2x+3)dx here we have to integrate then apply limit  integration of sinax = -cosax/a apply…

Q: an = arn+1 an = arn-1 * The general term of geometric progres Option 4 O anar" a" = arn-1 - Option

A:

Q: Consider a solid G, generated by rotating the region bounded by y = 2x² and y = 0 from would the…

A:

Q: bounded by the curve. Find the area y=2x+₁²₁ y=10x-x²

A: Given:  the curve is y=2x+12                               y=10x-x2

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A:

Q: Consider the double integral f(x,y)=(x²+y2)3/2 over the region R where y is bounded between 0 and…

A:

Q: Consider the following. 8x2 − y5 = 3 (a) Find y ′ by implicit differentiation. y ′ =    (b)Solve the…

A:

Q: Solve: y'' + 4y' = sin (2x)

A:

Q: 17. Use the method of disks/rings to determine the volume of the solid obtained by rotating the reg…

A:

Q: Which proper integral would you use to help determine the convergence/ divergence of the series and…

A: Integral test of convergence:Consider an integer N and a function defined on the unbounded interval…

Q: Use the table of Laplace transforms to find the Laplace transforms of the following cos² 2t sint cos…

A: Topic:- Laplace transform

Q: The value of the definite integral is Select one: O none of the others 45 6 30 -30 [² (3x² - 2x (3x²…

A: Topic = Integration

Q: (a) Find the integral of 6.x8 √21° +7 dx. **IDENTIA YAMIMATIO

A:

Q: The symmetric equation of the line that passes by P(1, -1, 1) and Q(3, 2, -1) is: Select one: x-1 0…

A: This question can be solved using the concept of lines in three dimensional geometry.

Q: Find all the values of x such that the given series would converge. (8x)" n11 n=1 The series is…

A:

Q: Locate the stationary point of the function z = 3x² + 4xy + 3y² (solve) Saddle point Maximum point O…

A: To locate the stationary point of the given function.

Q: Integrate (sinx + cos^2x)^3 dx

A: To evaluate: ∫sinx + cos2x3dx Let I = ∫sinx + cos2x3dx ⇒I =…

Q: True or False: We have Select one: True O False 2 x² dx > 2 [₁² x x³ dx 3

A:

Q: * Convert the polar equation to rectangular form r=7 (solve) x² + y² = 7 x=7 O Option 4 x² + y² = 49…

A:

Q: 3. Let f(x, y) = x³ 3x² + xy +7 and u = 0.6i + 0.8j, then find Duf(1,-2).

A:

Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: X = [₁,√38² - 1 db y = v √314 - 1 dt, -2 ≤x≤-1

A: Firstly find  derivative of y then find length of curve

Q: dz 10. Evaluate the integral where C is a simple closed curve cz(z - 1)' in the positive direction…

A: The integral ∫Cdzzz-1, where C is the simple closed curve in the positive directionthat contains the…

Q: Let à = and b= . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

A:

Q: Find the value So X (x²+1)= dx

A:

Q: 8 Find the sum of the series. Σ4¹/n-41/(n+1) answers. n=1 Give reasons for your

A: We have to find the sum of the given series.

Q: Q3: Let L be the line of intersection of the planes 3x + y -z = 4 and 5x + y + 2z = 1 Find the plane…

A: