y = -x² + 13 and y = x² + 5

Q: Find the constant a such that the function is continuous on the entire real line. - [8x², a = ax -…

A:

Q: Find the derivative of f(x) = (-x6 - 3x² - 6x) sin(x). Provide your answer below: f'(x)=[

A:

Q: The graph below is the function f(x) 543 -5 -4 -3 -2 -2 2 1 I 2 lim I→2 -1 -2- -3- -4 Select all…

A: In this question, we want to select all the correct options by the given graph.

Q: . (D³ - D² - 4)y = 0

A:

Q: F(x, y) = (3x-4y2i+6yj by the force in moving a particle in the positive direction once around the…

A:

Q: 8 Σ η=1 1 3Vn + n η

A: Calculate the limit of the given term as n reaches infinity.

Q: Find an explicit solution dyy² dx x² - 1 of the given initial-value problem. y(4) = 4

A:

Q: What is the area of the region between the lines y = 6x and y = 3x from x = 1 to x = 5? Select one:…

A:

Q: To find the arclength of y = 4x² - 3 from a = 0 to x = 4, which is the correct integral? √ VI + Sada…

A:

Q: a. In a geometric progression the sixth term is 8 times the third term and the sum of the seventh…

A: nth term of the Geometric progression , an= arn-1. Note : As per Our Guidelines , we can solve…

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

A:

Q: Find the function f(x) = ax³ + bx² + cx + d for which f(-3) = − 92, f( − 1) = 2, f(1) = 8, and f(2)…

A:

Q: Find the general solution of the following differential equation. y" + 14y' + 50y = 0 NOTE: Use C1,…

A:

Q: If the curve y= from (0, 0) to (3,9) is rotated about the x-axis, the integral that represents the…

A:

Q: Determine whether the statement is true or false. If f and g are discontinuous at x = c, then so isf…

A: 1. If f and g are discontinuous at x=c, then so f+g. 2. If fx is continuous at x=c, then so is fx

Q: D) 5

A:

Q: Write the product as a sum: 20 cos(136)sin(116) =

A:

Q: Evaluate the limit of a. 3 b. O tan 2x-2sinx as x approaches to 0. c. Undefined d. Infinity

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: question b

A:

Q: Solve the system: (combined method) x² + 2xy-y² = 14 x² - y² = 8

A:

Q: Evaluate: f 4dx 3x+2

A:

Q: The function f(x) = 2x³ − 33x² + 60x + 8 has derivative f'(x) = 6x² f(x) has one local minimum and…

A: Explanation of the answer is as follows

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate lies above…

A: Solution: ∬∫E z dV z = x2 +y2  ,     z =4

Q: Evaluate the given integral by making an appropriate change of variables. J 9 X - BY DA, where R is…

A: NOTE: Refresh your page if you can't see any equations. . where R is the parallelogram enclosed by…

Q: 3. State the remainder when f(x) = 2x² −x³ +1 is divided by (x+1).

A: We can find the remainder as below.

Q: etermine the total differential of the function, f(x, y, z) = 2x³ + 5y¹ − 6z Odf = 6x² dx + 20y³dy -…

A: Please refer to the image below

Q: Find the volume of the solid region in the first octant inside the cylinder x²+y2=4 and between the…

A:

Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

A:

Q: Suppose dt = and P(1) 4. Answer the following.

A:

Q: Justify your answer. n=1 test, ratio test, root test The series onverges (converges, diverges) by…

A: To find by which test the given series converges or diverges.

Q: Graph the circle. (x − 3)² + (y+ 1)² = 16 R -8 46 DE 3 23 -6- -8- 61

A: Standard equation of circle is ÷ x-h2+y-k2=r2 Where,h,k=center of the circle and  r= radius of the…

Q: The gradient vector of the function f(x, y) = cos(4x - 6y) is (4 sin(4x - 6y), -6 sin(4x - 6y)).…

A:

Q: Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = 1 if x = 0 if x =…

A: Given that a function f(x) and we show that the function has removable discontinuity at the origin .…

Q: Find the area bounded by the given curves. ')y=x3, y=x2

A:

Q: Question 10 Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1.

A:

Q: Find real numbers a, b, and c such that the graph of the function y = ax²+bx+c contains the points…

A:

Q: Express the complex number -3i in the form R(cos(0) + i sin(0)) = Ree where R> 0 and 0 ≤ 0 ≤ 2.…

A: The given complex number is -3i

Q: f(x) = x+69 (x-3)(x-6)

A:

Q: g(x) = -6x5 (1+x6)²

A:

Q: Suppose the function y=h(x) is nonnegative and continuous on [x3], which implies that the area…

A: We want to find area bound by the astroid

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. | sin (2) x²…

A:

Q: Calculate dz/dt given the following functions. Express the final answer in terms of t. f(x, y) =…

A:

Q: Question 11 Consider [x cos²x dx − x sin³x dx = = x+ƒ(x) + — 8(x) + - +C. What is the value of f 8

A:

Q: a) cot()

A:

Q: [x³e'dx,

A:

Q: Use partial fractions to find the power series of the function: 8 n=0 11x² + 629 (x² + 64)(x² + 49)

A:

Q: Find the average rate of change for the given function over the indicated values of xx. If…

A: Given that  y = -2x2 +5x+1   where 'x' goes from -2 to 6 .     we have to find average rate of…

Q: If the function f(x) is a quadratic function, then f(x) must open x-intercept(s). and have ii The…

A: If function f(x) is a quadratic equation, Then f(x) changes direction once.

Q: Find the area under the graph of the function over the interval given. 3 )y: [1, 31

A:

Q: Determine whether the vector field is conservative. F(x, y) = xe(x^2)3y(2yi + xj)   If it is, find…

A: