2 Y = x ²² - K² K is a constant X² + K² K is

Q: Find the derivative, but do not simplify your answer. y = (x² + x + 1)(³√x − ²√x + 2) y' = X

A:

Q: Compute the length of the curve r(t) = (-4t, 5t — 9, —8t - 4) over the interval 0 ≤ t ≤ 5 L =

A:

Q: Question Given f(x) = -2x2 + 4x + 13, find f'(-4) using the definition of a derivative. Provide your…

A:

Q: An isosceles triangle is inscribed in a semicircle, as shown in the diagram, and it continues to be…

A:

Q: Consider the path r(t) = (8t, 4t², 4 ln t) defined for t > 0. Find the length of the curve between…

A:

Q: Question Determine the intervals over which the function shown below is continuous. Enter your…

A:

Q: Determine the point(s) at which the given function f(x) is continuous. 9. x-9 f(x)= -2x Describe the…

A: We can find the answer in the below steps.

Q: The function f(x) = x³ + 5x²-√x + 1 is a polynomial of degree 3.

A:

Q: A tank of volume 0.30 m³ and height 1.5 m has water flowing in at 0.06 m³/min. The outlet flow rate…

A: We have to determine time t.

Q: 1.) f(x)=(2x-5)(3x-4)

A:

Q: The graph of f(x) is shown below. Which of the following statements are true? 8 7 60 5 4 3 2 1 M -8…

A: Ax x=6, limx→6-f(x)=limx→6+f(x)=f(6)

Q: f(x)=square root x+7, g(x)=square root x-5 Find the function fg and then determine the domain

A: Given fx=x+7, gx=x-5

Q: Transform the following equation of ellipse in standard for 7x²-10v² 56x +100y +278=0

A: 7x2-10y2-56x+100y+278=0 We have to convert into standard form. Lets first make a perfect square in x…

Q: dy dx + 2y = f(x), y(0) = 0, where f(x) = 1, 0≤x≤

A:

Q: A die is rolled. Find the probability of the given event. (a) The number showing is a 2; The…

A:

Q: 9. y² = 4ax

A:

Q: Find y' if y= - 14 3 X

A:

Q: 2. Graph and find the vertical asymptote of the function: x² + 1 3x - 2x² y =

A: Giveny=x2+13x-2x2

Q: Differentiate the function. f(x) = (2x6 - 1)22 f'(x)

A: We can find the answer in the below steps.

Q: Suppose that f(x) is continuous on the closed interval [a, e] such that a<b<c<d<e, and Sa f(x) dx =…

A: We have to find the integrals by using sum and difference rule of integration.

Q: If an object moves along a line so that it is at y = f(x) = 5x² - 2x at time x (in seconds), find…

A:

Q: Consider the following. f(x) = 5 - 2x² - (a) Find f'(x). (b) Graph both f(x) and f(x) using a…

A:

Q: S dx 2 (1+x²)²

A:

Q: a. Graph f(x) = 4-x², X#2 = 2. 4₁ b. Find lim f(x) and lim f(x). X-2* x X-2 c. Does lim f(x) exist?…

A:

Q: Find the speed at the given value of t: r(t) = (et-5, 12,5t-¹), t = 5 v(5) =

A:

Q: Consider the curve r = (e-4t cos(-t), e4t sin(-t), e-4t). Compute the arclength function s(t): (with…

A: To find the Arc length of the function.

Q: Consider the following. Function Point (V₂ (a) Find an equation of the tangent line to the graph of…

A:

Q: For what values of k will the system of equations have: refer to the data below and show complete…

A: A system of linear equations Ax=b has  (i) Unique solution if Rank of augmented matrix [A:b]=Rank of…

Q: Find r(t) u(t). . r(t) = (5t4)i ³j+2k u(t)= t²i4j+t³k r(t)u(t)= Is the result a vector-valued…

A:

Q: Transform the following equation of ellipse in standard form. 4x²-4y²-8x-8y-19 = 0

A:

Q: If y = (Inx)² + 15, find dy dx

A:

Q: Differentiate the function. h'(x) = = h(x) = 5(x5. 5(x52x3 +3)8

A:

Q: Q3. For the following matrices find x, y, z, and w, then check your solution. (2x + 5y)] 5y)] 2 6…

A: Need to find out the value of x, y, z, w.

Q: Find the solution of the differential equation y(t) = 1 t { x + + + ² ( ² ) * - ** (²) * <4 sec y =…

A:

Q: Evaluate the following expressions (note, you may not leave your answer as an algebraic expression):…

A: To evaluate the following expressions.a e3 ln5b 102 log105c log3278

Q: Find the solution of the differential equation (1 + y²)dx + (1 + x²)dy = 0

A:

Q: Q2. Using cylindrical coordinates to find the volume of the region bounded below by the cone z =…

A: Given, z=√(4x2+4y2) and plane z=2 Cylindrical coordinates are x=rsinθ and y= rcosθ x2+y2=r2

Q: Consider the function f(x) = x² + x and the point (1, 2). (a) Find the slope of the tangent to the…

A:

Q: 8 CO 6 X G 51 Co MAH 40% +++ BIAN 013 FOR 7 CO

A:

Q: Find the equation of the plane containing the point (-4, 6, 1) and parallel to the plane 6x7y2z = 0.

A:

Q: Q2. Using cylindrical coordinates to find the volume of the region bounded below by the cone z =…

A:

Q: Determine the point(s) at which the given function f(x) is continuous. f(x)=√√4x+20 Describe the set…

A: Given function:- fx=4x+20

Q: Find the indicated derivative. q² +2 6q — 2 dp dq = dp for p = dq

A: Given :- p=q2+26q-2

Q: If f(x)= 3x +41, which of the following is true? Select one: O a. f is not continuous but is…

A: Let's find function is continuous and differential at given point.

Q: Find the derivative of the function. 3 2 + X g(x): = X + 93√x

A:

Q: Q2. Using cylindrical coordinates to find the volume of the region bounded below by the cone z =…

A:

Q: 3x² - y2 + 18x-2y-10=0 4x²-4y²-8x-8y-19 = 0

A: Given Equations:- 1. 3x2-y2+18x-2y-10=0 2. 4x2-4y2-8x-8y-19=0

Q: Sketch the interval (a,b) on the x-axis with the point c inside. Then find the largest value of 8>0…

A:

Q: Find the domain of the functions below. f(x) = √x + √5 − x h(x) = (x − 4)−1/4 Enter your answers…

A: Formula: Domain of a square root function: f(x)= √y  can be find by y≥0

Q: Consider the following. f(x)= 12-3(1-x²)4/3 (a) Find f(x). f'(x) = (b) Graph both f(x) and f'(x)…

A: