A piece of rectangular sheet metal is 24 inches wide. It is to be made into a drain gutter by turning up the edges to form parallel sides. Let x represent the length of each of the parallel sides.

Q: 2-x x² if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist. f(x) = Let…

A: we will find the limit.

Q: Q3: What are the ways tha

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Q: How did dy dx Show solution pls. ty became d dx (xy)

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Q: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its…

A: Given :-x=2+t,y=3+12t and Tx2,4=5,Ty2,4=3

Q: Solve the given equation on the interval 0 ≤ 0 ≤ 27: tan 0+1=0

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Q: Sketch the graph of the function. [21x if || ≤ 1 if || > 1 f(x) ) = {2시 -3 -2 -1 -3 -2 -1 4 2 -2 y…

A: Topic - graph of a function

Q: Make a table of values for the equation. y = 5x X -2 1 1 2 || y Sketch a graph of the equation.

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Q: [1 2 3] Find A-¹ if A=4 1 5 L6 0 21

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Q: Find the equation of the line tangent to the curve f(x) = 4x² - 6x +39 at x = 1.

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Q: If your weekly cost, C, (in dollars) to manufacture L laptops and D desktops is: C(L, D)= 5000+50L…

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Q: se the isosceles right triangle and the 30°-60°-90° triangle to complete 45 r √2 - 45 60⁰ 30% √3

A: Part 1 :  For triangle                  For θ=30° It is right-angled triangle.…

Q: Find the domain of the function. (Enter your answer using interval notation.) √x 8x² + 7x1 g(x)= =

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Q: Q5: A. By power series, solve the ODE y' - 2xy = 0.

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Q: 4. Evaluate y ds where C is the upper half of circle x² + y² = 9, traversed in the counterclockwise…

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Q: B. Determine the center and the radius of the circle described by each equation. Then, sketch its…

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

Q: b) If x(0)=5, what is x(1)?

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Q: 6a + 24 3a-24 2 으 - a -16 a ²-2a-48

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Q: Find the shortest distance between the (entire) line L1 passing through the points A(1, 1, 2) and…

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Q: 1. Given: F(x)= 3x²+x-4, G (x) = 1-x' and H(x)= Find the following. H(-4) F (0) G (-5) a. b. C. x +…

A: As per our guidelines we are allowed to solve only 3 sub-parts. kindly repost others. THANK YOU.…

Q: For each function below, find the derivative. DO NOT use decimals in your answers. If f(x) = 2x5…

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Q: 11. A = {a, e, i, o, u} 12. B = {2, 3, 5, 7, 11, 13, 17, 19, 23,... } 13. C = {1, 3, 5, 7, 9, 11,…

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Q: 16. Solve the inequality. Write the answer using interval notations. (1 − x²)²³(2 – 3x²) – (2x −…

A: Given inequality:- 1-x2322-3x2-2x-x31-x212-3x1-x23>0

Q: 5. Find and sketch the domains of the functions of two variables below. Sketch the boundary with a…

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Q: In Exercises 1-8, find the domain D of the function. Give your answer in interval no X 1. f(x) = 3x³…

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Q: 4.Find all complex numbers of the form z=a+bi, where a and b are real numbers such that zz = 25 and…

A: To find out all the complex numbers for the given condition.

Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.

Q: A) x4-(y-1)4 lim (x,y)→(0,1) x²+(y-1)² = 0

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Q: 6. Find the area of the region enclosed by the curves x = 3 - y² and x=y_+1.

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Q: Find the indefinite integral by using the substitution x = 6 sin 0. (Use C for the constant of…

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Q: Compute the definite integral. ? 0 6ex sin(x) dx

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Q: 1. 15mg of Carbon-14 decays at a rate of .012% continuously a. How long until you are down to 10mg…

A: Given problem:- 1. 15mg of Carbon-14 decays at a rate of .012% continuously a. How long until you…

Q: ƒ(x)—ƒ(6) f(10) c) f(x) = =

A: To find f(x)

Q: Can someone explain tangent for more as well as limits. *all of this within calculus *

A: Please see the below picture for detailed solution.

Q: Find the volume of the solid obtained by rotating the region bounded by y = x and y = √√x about the…

A: In this question, we need to find the volume of the solid.

Q: 5. Find all constants a, b that make f continuous everywhere. (Use limits and definition of…

A: With the help of limiting criteria we have to find the values of a and b.

Q: solve the equation  2×+6-4(×+1)=3×+5

A: This question can be solved using the concept of solving linear equation in one variable.

Q: H(t) = -15 16 -15 - +² Sketch the graph of the function. 4-t - 10 - 10 -5 -5 H(t) 20 15 10 $5 H(t)…

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Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

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Q: The point  P(9, −2)  lies on the curve  y = 2/(8 − x). (a) If Q is the point  (x, 2/(8 − x)),  use…

A: The point on the curve y = 28-x is Px1, y1 = 9, -2 Another point Q on the curve is Qx2, y2 = 8.9,…

Q: Use Green's Theorem to evaluate 90 O O -384 O -48 fayd r²y² dr + (yr³+ y²) dy where C' is shown…

A: As we know from Green's theorem: ∫cMdx+Ndy=∫∫R∂N∂x-∂M∂ydA Where, ∬dA=∬dxdy or ∬dydx And We know the…

Q: 1337 (2) =?

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Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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Q: Consider the differential equation (xy + 3x − y − 3) dx = (xy − 2x + 4y − 8) dy. By separation of…

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Q: Find the solution of the differential equation (6x² − y + 3) dr+ (3y² - x - 2) dy=0 1 O x + O 2x³ O…

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Q: Consider the integral 2³ In(a) dz: Applying the integration by parts technique, let u = ln(2)…

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Q: For the function f graphed in the accompanying figure, find the following limits. If a limit does…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (a) Find the Taylor series expansion of the function cos x around x = 0 (b) Use the first three…

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Q: What does it mean, graphically and algebraically, for an equation to be even or odd? How would you…

A: we will do as required.

Q: Find the domain of the function. (Enter your answer using interval notation.) G(x): 8x + x X Sketch…

A: Solution ) G(x) = (8x + |x| )/x G(x) = 8x/x + |x|/x  G(x) = 8 + |x|/x  If x = 0 G(x) = 8 + 0 = 0 If…

Q: R is the region bounded above by the function f(x) = −4+7 and below by the function g(x) = - + 2…

A: We need to draw graph.