Find the point(s) on the curve y www 10 closest to the point (0,9). The point(s) are separated by commas) Enter here (using math notation or by attaching in an image) an explanation of your solution. (if there is more than one closest point, enter the points

Q: 8. DETAILS A rectangular storage container with an open top is to have a capacity of 101 in.³. The…

A: Here we have given a rectangular storage container with a capacity of101 in3. And the length of the…

Q: Let S(x)=In(x² - 4x+5)

A: first derivative

Q: Consider the graph of f'(x) given below. At what value(s) of x does f(x) have a local minimum? If…

A: Topic - Local minimum of a function. Local minimum of a function: from f'(x) ,we can find local…

Q: Write the first three terms of the sequence whose nth term is given by the formula. 1. an-n-1 1 4n…

A: To find the first term , we need to substitute n =1 in an . For second and third term substitute n=2…

Q: Given f(x) f(x) = ln (√x² + 3) find f'(x) f'(x) =

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x-² In(x),…

A:

Q: Given k(x)=f(x)g(x), what is k'(8) ? 1 6 -5 -4 3 2 0 O-1/3 2/3 O-2/3 O 10 tio 1 2 3 4 I 1 f 5 1 6 7…

A: Graph of the functions f and g is given and kx=fxgx. We have to find the value of k'8.

Q: Rewrite the following equation in logarithmic form using the natural logarithm (ln). Hint: you will…

A:

Q: Find the equation of circle with Centre (2, 2) and passes through the point (4,5) - Find the…

A: Topic:- geometry    Note :- as per our guideline if more than one question uploaded than only first…

Q: A factory manufactures three products, A, B, and C. Each product requires the use of two machines,…

A: We have to set up the linear programming problem.

Q: Given f(x) = 2 sec (x), write the equation of the line tangent to y = f(x) when x = 5п 6

A:

Q: Compute the line integral of the vector field F = (3zy-¹, 4x, -y) over the path c(t) = (et, et, t)…

A: see below the answer and calculation

Q: If f(x) = 6 ln(8x + 7 ln(x)), ƒ'(x) = ƒ'(1) =

A:

Q: If f(c) is defined (meaning the value exists), then f is continuous at x= c. True False

A:

Q: what if it's going up by ten percent more ? not 10$

A:

Q: 3. For each of the following equations, find the general solution using the method of varia- tion of…

A:

Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an Since lim…

A:

Q: I Let f(x) = -12 (1) ² +8. Evaluate f(-7). 22 ƒ(−7) = Number

A:

Q: Q4. Evaluate the limits of the following functions as x → 0 sin² x x² (a) f(x) = e (b) f(x) = x ln…

A: L'Hospital rule:- If a function f(x)=p(x)q(x) has the limit 00 form then limx→0f(x)=limx→0p'(x)q'(x)…

Q: Consider the following function. f(x) = x³ + 3x² - 45x + 9 (a) Make a sign diagram for the first…

A:

Q: Solve for x. 32x+24 (3*)-81=0 Round to the nearest hundredth if necessary. If there is more than one…

A: Given query is to find the value of x.

Q: f(x)=3x2+2x-5 g(x)=x2+7x-2 7 A BI

A: Given query is to solve the system of equations.

Q: The DE (-7ln(2y) - 4ex) dx = x = ( 7x + 2y) dy у is an exact differential equation. Select one: O…

A:

Q: Express f(x) in the form f(x) = (x-k)q(x) +r for the given value of k. 3 2 f(x)=x + 7x + 11x + 2, k…

A:

Q: 1) Consider an investment of $3000 at 2% compounded monthly. Find the amount in the account after 4…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Match each function with its derivative. f. 7. cos(x) + 8 X Y • x² + 3x 2.8 +7√x 4 sin x + x x7 . .…

A:

Q: State the domain, vertical asymptote, and end behavior of the function. Enter the domain in interval…

A: Please see the below picture for detailed solution.

Q: A. Orthogonal Trajectory: For the family, x² + 3y² = cy, find that member of the orthogonal…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: (b) Use the gradient to find the directional derivative Du f(x, y, z) of f(x, y, z) = sin(3x) cos(8y…

A:

Q: 2

A:

Q: If a, b, c are the sides of a triangle and is the included angle between aand b, find and by…

A:

Q: Evaluate the integral where D is the region within the cone z = x² + y² S S S₂ ( x² + y² + 2² )³¹ dv…

A:

Q: A. If f¹(x) = 2x¹/7 – 1 find f(x) -

A:

Q: 2. Eliminate the arbitrary constant(s) in the following equations: a. y C₁x²2+ C₂x + C3 b. tany C₁…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: Determine whether the table could represent a function that is linear, exponential, or neither. If…

A:

Q: Find f(t). f(t) = <{{ e-s s(s+ 1) | +( | ) u(t -|

A: Given:     ℒ-1e-sss+1 Apply inverse transform rule: If      ℒ-1Fs=ft then  ℒ-1e-asFs=?t-aft-a Where…

Q: If f(x)= f'(x) = f'(1) = places) tan x - 3 sec x > Next Question (round to 3 decimal

A:

Q: Consider the following function. f(x) = x² + 4x³ + 14 (a) Make a sign diagram for the first…

A:

Q: Find and classify the critical points of the function f(z,y) = y^-32y

A: Solution: f(x,y) = y4-32y+x3-x2 Critical points are points where the function is defined and its…

Q: Consider two positive numbers x and y such that x + y = 58. Maximize and minimize the quantity y…

A:

Q: How many solutions are there to the system shown in the graph below? 5

A: How many solutions are there to the system shown in the graph?

Q: Determine the maximum area of a rectangle inscribed in the ellipse+ = 1. Enter only the maximum area…

A:

Q: Suppose the function y = f(x) is defined by an equation x² + y² + sin(xy) = 9. Given that f(0) = 3.…

A:

Q: Find the slope of the tangent line to the curve below at the point (1, 7). √3x +2y + √5xy =…

A: NOTE: we can answer up to 3 subparts only. . take derivative on both sides

Q: Find the arc length of the curve below on the given interval. y=2x³/2 on [0,9] Which of the…

A:

Q: Find the area of the region bounded by the graphs of y = x² x and y = 2x from x = -2 to x = 4.

A: Given y = x2 - x y = 2x from x = -2 to 4 Area of region bounded = ∫x1x2( y2 - y1 )dx

Q: Mark the critical points on the following graph. x³e-7,2 Те -5 -4 -3 -2 Clos ALL 10+ 8 6 4 2 -2 -4…

A: Please see the below answer.

Q: e)- Assume that now | x1 = R. Show that x-X=0 [Hint: Differentiate constrain't ev]. Deduce that I is…

A: It is given that: X⇀=R so, we get, X→2=R2

Q: Question 4 Use logarithmic differentiation to find the first derivative. Enter your answer without…

A:

Q: Is the graph of g(x) = 4x³ + 9x² + 7x + 3 concave up or down at the point with X-coordinate -2?…

A: g(x)=4x3+9x2+7x+3