of the function given by the equation derivations details.

Q: Find the directional derivative fü(9, 2) for the function 37 - 47 5 f(x, y) = xy + y³ with u = fű(9,…

A:

Q: + y² x² + y² = 64 from x=-1 to x=-3 Find the length of arc of the curve x²

A: Given: x2+y2=64 From the limit  x=-1 to x=-3 To obtain the length  of the arc:

Q: 6. Determine the 19th derivative of the function y=sin(x). Fully explain the process you used to…

A:

Q: A room in a certain factory wanted to improve the CO₂ concentration level which is a high 2500ppm.…

A: The air inside has 2500 ppm of CO2 and volume of 5000 cu.m  Fresh Air has 400 ppm of CO2    Now, let…

Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…

Q: Find the equation of the tangent to the curve y = sin(3x) COS(z) at z = 4.

A:

Q: 3. Including all steps, charts, and derivations details, use the curve sketching methods to sketch…

A:

Q: Find the first four partial sums and the nth partial sum of the sequence an 2 30 an =

A: Given function is an=23n Here, we have nth term of series Evaluate the first termS1, substituting…

Q: An investor has $10000 to invest in either a bond that matures in 5 years or a business that will…

A:

Q: Write the following expression as one integral. 3 5 3 [ -6 f(x) dx + f(x) dx - f(x) dx 0 0 3 5 3 $…

A:

Q: Rewrite sin(x+ H Enclose arguments of functions in parentheses. For example, sin (2x). sir 20 in…

A:

Q: Solve the following inequality: 2x + 4 8 x < 16 x < 10 x < 8

A:

Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform  thickness. If the…

A: Given data:- The diameter of the iron ball is, 8 cm The thickness of the coating is, 2 cm The rate…

Q: Find the domain and range of the function.   ​G(t​)=1/t2-25

A: Given,            Gt=1t2-25To find : Find the domain and range of the function.

Q: Evaluate the definite integrale dr.

A:

Q: √x+9 at x = 0. Write your answer in the form a+bx+cnx" n=2 where a, b, and each cn are constants.…

A:

Q: 1.5: The area of the region enclosed by the graph of f(x)=√x and the x- axis on the interval [0, 4]…

A: Area bounded between the curves : Consider the curve y=f(x) and x-axis on the interval a,b , then…

Q: Use cylindrical coordinates to integrate f(x, y, z) = z over the intersection (i.e. all the volume…

A:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) 13 + 9x -3y…

A:

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7.

A:

Q: Find the nth term of a sequence whose first several terms are given. 10 11 9' 10' 11' 12' an = Need…

A: The given sequence is 89,910,1011,1112,....

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of y=-x² + 7x between x = 1…

A:

Q: Factor the following expression: x^2 +9x + 8 (x + 1) (x + 8) (x - 1) (x - 8) (x - 1)…

A: Solution

Q: Evaluate O O In O In In a:² In |-2|³ |x + 1/² x+2/8/3 |x-1/5/3 O 3 ln x²-x-2+C x-1/5/3 x+2/8/3 x+7…

A: We have to evaluate ∫x+7x2-x-2dx.

Q: Find the indicated value. f (2,3) if f(x,y) = 4x²y - 2xy³ f (2,3)= (Type (Type an integer or a…

A: fx represents the partial derivative of the function f(x,y) with respect to x. Also fx(a,b) is the…

Q: 3: The derivative of the function sin(cos x) is a) cos(cos x) b) cos(-sin x) c) sin x cos(cos x) d)…

A: Here we have to use the concept of derivatives

Q: 2. xem di

A: The given integration, ∫xe3xdx use integration by parts, ∫u dv=uv-∫v du use the formulas,…

Q: For the function f(x) = two periods. Amplitude: A Period: P = -2 sin HARE Number Xx 37 4 Enter the…

A:

Q: Find the sum of the first four terms of the series. S4= (-1)^(1+3)*1+(-1)^(2+3)*(1)/ (Remember that…

A:

Q: Let y = 5√√/T. Find the change in y, Ay when x P 3 and Ax 0.2 = Find the differential dy when x = 3…

A: Given the function y=5x

Q: 40 For problems 21 function to find t C 123, use the following. following rut o

A: We will find the required.

Q: Based on this graph, what is the solution to the system of equations? (3, 2) (2, 3) There are an…

A: Topic:- application of geometry

Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

A:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. 3 + 6x3/2 f(x, y) R:…

A: In this question, we need to find the area of the surface.

Q: dx 3 sin x-6 cos x

A:

Q: a) 2+ 3i b) 2-3√2i Write in trigonometric form with 0 ≤ 0 ≤ 2π

A:

Q: Need Help? TEACHER How long will it take for an investment of $3000 to double in value if the…

A:

Q: Find the derivative of y with respect to x in the following equation y = 1¹ where u = 1-z O x² O-x²…

A:

Q: Find the area bounded by the curve xy=2 and the line x+y=3 O 0.11 O 0.17 O 0.22 0.05

A:

Q: system, or show that it is inconsistent. (If the system has in = z(t), and w = t. If there is no…

A: Given system can be written as  101201-2012-10213-2xyzw=1130 Augmented Matrix…

Q: Which system of equations represents the following word problem? Carla has 15 nickels and dimes for…

A:

Q: Use basic identities to simplify sin³ x + x + cos²x sinx. Enclose arguments of functions in…

A:

Q: Solve the differential equation dy dx y²+7xy+16x² x² O a. x - y = O b. x + y 5 (y + 4x) In y O C. X…

A:

Q: 8. Find the stationary points of the following functions and classify them as relative maxima,…

A:

Q: Use the limit definition to find the instantaneous rate of change of f(x) = 3x^3 - 4x at x= -3

A: Question is solved.

Q: 17. f"(6) and f" (a) $(0) = (0) ³+4 (6) ³ + 2 Ans: f(0) = 2 for Problems 18-20 use the following…

A: Question : for problems 18-20 use the following graph. 18 . Largest open interval from where…

Q: What are the parametric equations of x - 2y + 3z - 1 = 0?

A:

Q: Two cars are moving towards an intersection. One car is 150 meters north of the intersection and…

A:

Q: Find the partial sum S, of the arithmetic sequence that satisfies the given conditions. a2 = 9, a5 =…

A:

Q: A company manufactures mountain bikes. The research department produced the marginal cost function…

A: