Find the area bounded by curves y = -4 + √x and y = -16 + x 4 (Round your answer to two decimal places.)

Q: 3) Use the method of Lagrange multipliers to find the points on the curve x²y = 2 nearest the…

A: The given equation of curve is Let the point  on the curve which is closest to origin

Q: Please answer the following: Thanks Given 6xy= 2 + y² , a) Find the coordinates of a point…

A:

Q: Let y = f(x). Begin by finding the derivative of f(x) = -x³ + 6x² - 3. 3 F'(x) = (x³ + 6x² − 3) d dx…

A: The objective of the question is to find the second derivative of the function f(x) = -x^3 + 6x^2 -…

Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

A:

Q: Find y'' if y=-8 cos x. OA. y'=8 sin x OB. y'= -8 cos x OC. y'= 8 cos x OD. y'= -8 sin x

A: Explaination of answer is as follows

Q: Differentiate the functions: cosec x * cos x

A:

Q: Find F as a function of x and evaluate it at x = 0, x = π/4, and x = π/2. ftc F(x) F(0) F(x) I = =…

A:

Q: Time (secs) 0 30 60 90 120 150 180 Speed (mi/secs) 0.00 0.03 0.08 0.16 0.27 0.42 0.65 9. The table…

A: Given Information table is as follows

Q: d) Write an expression that represents the approximate value of g(x) for a generic value x in the…

A: The graph of the function g'(x) is shown as,

Q: (b) Use Desmos to graph the surface area function on the following coordinate system. Label each…

A:

Q: 13. If there are initially 2000 bacteria in a culture, and the number of bacteria double cach hour,…

A:

Q: What is the second derivative x³ - 5x² + x = 0? A. 3x² - 5x B. 10x-5 C. 3x + 10 D. 6x-10

A: The given equation is Let

Q: Write v as the sum of two vectors, one in Span {u₁) and one in Span (u₂,43,44). Assume that…

A:

Q: 7. Determine where fis discontinuous. Justify your answers. √=x if x < 0 3-x if 0<x<3 (3-x)² if x ≥…

A:

Q: 1. Find the area between the two curves. Be sure to show the representative rectangle in the 1st…

A: Given functions are,y=f(x)= 8 cos x and y=g(x)= sec2x

Q: A tall pipe is 30 feet tall. A person with a height of 6 feet walks away from the pipe along a…

A:

Q: Find an equation of the line tangent to the graph of G(x) = 3e The equation of the line is y=. at…

A:

Q: Express your answer as a polynomial in standard form. f(x) = -3x + 5 g(x) = x² + 2x + 15 Find:…

A:

Q: Find the domain of f(x). f(x)=√x² + 9x - 8

A: Here we will find the domain of the given function on solving the quantity under root putting…

Q: Given the definitions of f(x) and g(x) below, find the value of g(ƒ(8)). f(x) = X 11 g(x) = x² + 7x…

A: The given functions  and .The aim is to find the value of .

Q: 3 · [²³ F(x) Given 6 ³ fº f(x) f(x) dx = 9 and Exercise (a) 6 [° F(x) f(x) dx = -8, evaluate the…

A:

Q: Evaluate I = (sin x + 2y) dx + (8x + y) dy for the nonclosed path ABCD in the figure. y C B A=…

A: Here  we have to find the integral along closed path.

Q: Use the summation formulas to rewrite the expression without the summation notation. S(n) = k = 1…

A: The given series

Q: Find the area of the region bounded by: p2 = 72 cos 2

A:

Q: Evaluate: [8zº · sec² (25) dx =

A:

Q: Evaluate the following. log 6216

A: Let .We know that,

Q: 5. Example: The graphs of f and g are given. Use them to evaluate each limit, if it exists. If the…

A: A graph of the functions  and  are given.The aim is to find the following,(a) (b) (c) Note:  Since…

Q: 2 x² e ³+1 dx

A: We do only first part of multiple questions.please re-post other parts.

Q: 9.5 4.5 9.5 » [*¨* f(x)dx = 6, [^¹³ f(x)dx = 3, [ f(a)da = 3, [ f(x)dx = 8. 2 (Section 4.4) Suppose…

A: Find the integral 6f(x)-3, limit from 7 to 4.5.

Q: Find the volume of the solid obtained by rotating the region bounded by the x-axis, the y-axis, the…

A:

Q: 2. For f(x)=√14-2x (a). find the domain. Write your answer in interval notation. (b). Graph…

A:

Q: Find a, b, c, and d such that the curve y=ax^3+bx^2+cx+d has its tangent line at (1, 1) and at (0,…

A: To find such that the curve  has its tangent line at(1, 1) and at (0, -2) are parallel to lines…

Q: antiderivative. Use C for the constant of integration. 1 3 cos² (4x) F(x) = (In(|sec (4x) +…

A: Given The aim is to find the antiderivative of .

Q: Express the function as a power series by first using partial fractions. f(x)= 2x+5 x2+5x+4

A: Given: f(x)=2x+5x2+5x+4let's first factor the denominator and then use partial fractions.The…

Q: 5. If f(5) = 7.8 and ƒ' (5) = 5.2, then use the linear approximation (also called the tangent line…

A: The linear approximation of a function f(x) at x=a is given by

Q: Let f(x) = x if x ≥ 5 5 if x < 5 a. Find f(1), f(5), and f(7). b. Sketch the graph of y = f(x).

A:

Q: Consider the triangle below (not drawn to scale). ہے a= a Let b = 9, ZC = 40° and /A = 45°. Find the…

A:

Q: 2. Given the graph as shown, find the limits. lim f(x)= x → -2- A) B) D) E) lim f(x)= x-2 lim f(x)=…

A: The graph of the function is given.The aim is to find the

Q: Find the derivative of the function. (37) 2 S = sin 3nt 2 - COS

A: Given,

Q: Evaluate the indefinite integral as a power series. fin(1+x²) dx

A:

Q: Find the unit tangent vector T(t) at point P. r(t) = t²i + tj + 20 k, T(5)= X P(25, 5, 20/3) Find a…

A:

Q: At time t, the position of a body moving along the s-axis is s=13-1512+72t m. Find the body's…

A:

Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

A:

Q: Find the sum of the series: Σ n=1 2 (n + 6)(n + 4)

A:

Q: Consider the following. f(x) = 48x − 4x2 Find  f '(x). f '(x) =        Find the critical…

A: The objective of this question is to find the derivative of the function f(x) = 48x - 4x^2 and then…

Q: Estimate the area under the graph of f(x) = 1+x² from x = -1 to = 2 using six rectangles and right…

A: Given,from x=-1 and x=2

Q: Suppose that the variables x and y are related by the implicit equation X V = -3.3x 1.8 ln(x)+2.8y—…

A:

Q: x3 x² + 4x +3 Example: ₁ dx

A: We have to perform the partial fractions

Q: 19. If $100,000 is invested at 6% compounded monthly for 7 years, the compounded amount is given by…

A:

Q: 5. Using Geogebra, draw the polar curve, r = sin³ (2.50) +cos³(2.50),0 ≤ 0 ≤ 2ñ.

A: Consider the curve