Find all relative extrema and saddle points of the function. Use the Second Partials Test where applicable. (If an answer does not exist, enter D g(x, y) = x² - y² - 3x - 4y relative minimum (x, y, z) = relative maximum (x, y, z) = = saddle point (x, y, z)=

Q: Find the area of the surface obtained by rotating the curve about the y-axis. = (y² - Iny), 1 ≤ y ≤…

A: surface area  about  y axis  bounded by  x=g(y)Area=∫ab 2π g(y)1+g'(y)2  dy

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A:

Q: Analyze the continuity of this function. If there are discontinuities, state the type. x² + 2x x≤1…

A:

Q: Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y =…

A: This question is based on differentiation of parametric equation. Slope, m = dy/dx = {dy/dt}/{dx/dt}

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A:

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: Given curves , y=x2y=x5 For point of intersection x5=x2x5-x2=0x2(x3-1)=0x2=0  or x3-1=0⇒x=0 and x=1

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

A: Given: Volume of right circular cone is V= πr2h3 and dVdt=30 cubic feet per minute To find: dhdt

Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

A:

Q: 80 1 n+8 Does the series (-1) converge absolutely, converge conditionally, or diverge? n=1 Choose…

A:

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: graph is concave upward when f"(x)>0  and concave downward when f"(x)<0.

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A: Given the function f(x)=sinx2

Q: eased equipment worth $70,000 for 5 years. If the lease rate is 5.75% unded quarterly, calculate the…

A: Please refer to the image below

Q: (a) State a necessary condition for a vector field to be a gradient. (b) Determine if the vector…

A: (a)

Q: Given the integral below, find the best lower and upper bounds for F that the comparison theorem can…

A:

Q: Express your final answer at least three (3)decimal places. A particle moves with a velocity of…

A:

Q: Find dx dx 0.4 0.4 -3.3x-4+5x -4 -3.3x 5x ...

A:

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A: We can find discontinuity of the function .

Q: Question 8 Which of these is the volume of the solid of revolution generated by revolving the region…

A: Here we have to find the volume.

Q: Find the indicated quantities for f(x) = 2x². (A) The slope of the secant line through the points…

A:

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A:

Q: f(x)=1/(1-4x); 1.07-1

A:

Q: Which of the following rational functions is equivalent to the partial fraction decomposition 2x 2x…

A: 2x2x-1-3x3x-1=2x3x-12x-13x-1-3x2x-12x-13x-1=2x3x-1-3x2x-12x-13x-1=x2x-13x-1

Q: Evaluate the integral. Select the correct answer. O 3100 3100 3100 t + t + sin 16t+sin 32t+C 75 1…

A:

Q: Find the slope of the curve r = -5+5 cos 0 at the points 0= + Sketch the curve along with the…

A:

Q: Question 6 Find the area 2 y=x²-3 between the curves and y=x+3

A: In this question, we will find the area of the region bounded by the given curves.

Q: Find an integrating factor and solve the equation 4x y' = e¹x + 8y - 1.

A: Solution of given question is written in below steps.

Q: To evaluate the integral 3 100+ x² dx, which of the following substitution be used? Select one: Ox=…

A: Topic:- application of integration

Q: O Differentiate Y 2 +1 3/2

A:

Q: How much money should Nicholas invest today into a fund that earns interest at 4.75% compounded…

A:

Q: Find the outward flux of the field F = 2xyi + 8yzj + 6xzk across the surface of the cube cut from…

A:

Q: lim x→0 x⁹⁹ sin (7x) (sin x) 100

A:

Q: 1. The value of A. sin-¹(²*²+¹) + C 5 sin-¹(²*x+¹)+C B. C. sin-¹(+¹) + C D. sin-¹ (¹) + C 2x

A:

Q: Consider the series + (-1)" n=1 n Which of the following statements is true? The series is not…

A:

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A:

Q: Letf(x) = x² – 5x + 6, g(x) = 5x – 1, find the following: (1)(f + g)(x) = (2) (ƒ − g)(x) = - (3) (ƒ…

A:

Q: Find the area of the shaded region shown in the graph. The area of the shaded region is (Type an…

A:

Q: Use the shell method to write and evaluate the integral that gives the volume of the solid generated…

A:

Q: y" - 3y' = 8e^(3x) + 4sin(x)

A: The given differential equation is;  y''-3y'=8e3x+4sinx.

Q: Find h'(t) if h(t)= h'(t)= 3 1/2 3 3/5

A:

Q: Evaluate the definite integral given below. 2 [ ²³ ( -5x ² + 2x² ) dx

A:

Q: dy (1M1) Find dx 70x9 1+ 5x = sin(xcy²) I

A:

Q: 1. Write the x and y coordinates of any point on the unit circle in terms of the angle corresponding…

A:

Q: Determine whether the series DIVERGES.) 00 n=1 חל - 6 14" = n=1 6-77 147 129 Tutorial converges or…

A:

Q: x= 4+² +7, y=t, t = -1 Write the equation of the tangent line. What is the value of dx² d²y dx² at…

A:

Q: Evaluate the integral Select the correct answer. O ㅇ 12 πC 24 πC 12 + + + 나이 이어 나이 이어 1 4 −|◄ −|+…

A:

Q: 1. Find the area bounded by y = 4x-x, x+2 = 0 and y = 4 using vertical and horizontal strip

A: Solution is given below:

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: To find the value of dy/dt in first case and value of dx/dt in second case.

Q: Find the area of the region inside one leaf of the three-leaved rose r = cos 30. The area of the…

A: We have to find the area of the region inside one leaf of the three-leaved rose.

Q: At value of a does the curve y = 2√4x2+1 have a tangent line with a slope of 2? O √12 00 O /12 O…

A: To find the slop at given point.

Q: Alfredo and Alicia are having an ice skating contest. They skate along a long, straight track and…

A: