For the function f(x) = 12x – 10, find the slope of the tangent line at x = = 3.

Q: The population of Calculusville decreases by 5% each year. If the population of Calculusville was…

A: The population of calculusville in 2015 is, Rate of change,

Q: Graph the polar curve r = 2 + 4 sin до Select a curve and use the point(s) to adjust: O O

A: Here we have to draw the graph of the polar equation

Q: Find an angle in each quadrant with a common reference angle with 154º, from 0°<0<360° Quadrant I:…

A: An angle made by the terminal side of the given angle with the -axis is called the reference angle.

Q: O DOM x Nit dx

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Q: If AABC-ADEC, find the length of DE. A 7x B 24 21 4 26 16 20 12 15 3x+9 E

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Q: Given the series (4) Does this series converge or diverge? O diverges converges If the series…

A: Let's consider a series S as follows:Now consider a ratio r as follows:If  r&gt;1 then the series S…

Q: Minimize subject to: 2x + y ≥ x ≥ 0 y ≥ 0 -10 Select one: z = 4x + 5y 2x - 4y ≤ 10 15 -10- 10' x a.…

A: The common region satisfied by all the given set of constraints including the non-negative…

Q: Convert the point (x, y, z) = (2, -3, -5) to spherical coordinates. Give answers as positive values,…

A: Given point (x, y, z) = (2, -3, -5) To convert the given point to spherical coordinates we need to…

Q: Find an equation of the tangent plane at the given point. g(x, y) = exly, (7,1) (Express numbers in…

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Q: 2 lim (sin x) Inx *→0+

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Q: Solve and write interval notation for the solution set. Then graph the solution set. 6x≤ 36 or x-2>0

A: The system of inequalities is given as

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Q: Find the equation for the circle with center (2, -3) and passing through (1,2). Write the equation…

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Q: Q 30. If a ball is thrown into the air with a velocity of 30 m/s, its height, h in meters after t…

A: We have,      h(t) = 30t - 4.9t2 Find the instantaneous velocity when t = 2 seconds.

Q: Part. e. True or False: f(x) x = 3, x=- 3. = x-3 2 3x-8x-3 has two vertical asymptotes:

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Q: -5 -14 -2 Find lim -1- Find lim 2 ●1 #4-1+ J f (x) f(x) Find lim f(x) HI-1 -2 03 -$+ 2 Find f (-1)…

A: Explanation of the answer is as follows

Q: 31. f x +4 x² + 2x + 5 dx

A: Integration is a reverse process of differentiation.Use the

Q: The vertical asymptotes of the cotangent function are located at the same values of x for which the…

A: we want to determine the given statement is true or false .we can calculate the vertical asymptotes…

Q: 3- The cost function of a manufacturing company in order to produce x items is C(x) = 2 log (x + 2),…

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Q: 6x≤-36 or x-2>0 Select the correct choice below and fill in any answer boxes in your choice. OA. The…

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Q: Part. d. True or False: d 1 dx 3 X 1 2 3x

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Q: Find each of the given sets. Present your answer by listing the elements of the set. Make sure to…

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Q: -5 -44 43 -2 03 2 H -1 -2 03- Find lim f (x) Find lim f (x) x411+ Find lim f(x) HI-1 2 3 4 Find…

A: A function  is said to be continuous at  if .

Q: Consider the following curve. y = 2x² - 6x + 1 Find the slope m of the tangent line at the point (4,…

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Q: 6 Calculate [√6 (cos+ i sin)] and express the answer in simplest polar form with the argument from 0…

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Q: An aquarium 8 m long, 1 m wide, and 1 m deep is half-filled with water. Find the work needed to pump…

A: Given that an aquarium 8 m long, 1 m wide, and 1 m deep is half-filled with water.

Q: Evaluate the definite integral that represents the area of the surface generated by revolving the…

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Q: Set up the integral that uses the method of cylindrical shells to find the volume V of the solid…

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Q: Q4.1 According to Debye's formula in physical chemistry, the orientation polarization P of a gas…

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Q: Evaluate the indefinite integral: S e³x √1+e³x dx

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Q: 4(b) Consider the region in R3³ defined by the following inequalities: x₁ + 3x₂ + x3 ≤ 4, 2x1 +…

A: To write the linear system obtained from the given system of inequalities by adding non-negative…

Q: 2. Find the first and second derivatives. Simplify as needed. (a) f(t) = t sin t )=-=- (b) h(r):

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Q: A ball falls from a cliff at a height of 425 m. The ball's height, h. in metres above the ground…

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Q: Find all values of the parameter q such that (29-5) n+1 (i) For all q 5 O a.i. O b. ii O c. iii O d.…

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Q: Determine if a graph is a function. Is this the graph of a function? No O Yes -B Ay +2 Q

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Q: In this problem, y=1/(x2+c) is a one-parameter family of solutions of the first-order DE y + 2xy =…

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Q: Which equation represents the graph shown below? y 5 4 3 2 1 W -4 -3 -2 -1, 0 1 2 13 4 5 6 -1 -3 -4…

A: As graph cut negative y axis at x=0 ,so function value is negative.

Q: Find the domain of the function f(x, y, z) = √√ xyz². O A. Domain = {(x, y, z) ER³ : xy ≥ 0} O B.…

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Q: b. Evaluate—(3x − 2)° 6

A: We need to evaluate

Q: Determine whether the pair of lines is parallel, perpendicular, or neither. 9x + 3y = 12 27x + 9y =…

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Q: Let r(0) = (5 cos(0), 5 sin(0), 40). Find the decomposition of a(0) into tangential and normal…

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Q: A heavy rope, 90 ft long and weighing 36 lbs, hangs over the edge of a building 100 ft high. How…

A: Given heavy rope 90 ft long weighing 36 lbs over the edge of a building 100 ft high.We have to find…

Q: One of the steps to Gaussian Elimination is to multiply an equation by a zero constant. O True False

A: Multiplying an equation by a zero constant is not a valid step in Gaussian Elimination.

Q: Differentiate dx y=3x²+2 (3x² + 2) = 3+.

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Q: (a) Find the slope of the curve y=x²-3x-5 at the point P(2, -7) by finding the limit of the secant…

A: Given;

Q: (x(t) Find a plane containing the point (6,4,2) and the line y(t) = z(t) = = 4 + 4t 2 - 2t 2 - 2t

A: Line,x(t) = 4 + 4ty(t) = 2 - 2tz(t) = 2 - 2tPoint,(6, 4, 2)

Q: 400 For the demand function q = D(x) = X -, find the following. a) The elasticity b) The elasticity…

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Q: 55. x³y"" - x²y" + xy' = 0 C

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Q: Let f(x)= 1+ 4x 5- 2x (i) What is the domain of f(x)? (ii) What is the range of f(x)? (iii) Find the…

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Q: A 40 inch wire is to be cut. One piece is to be bent into the shape of a square, whereas the other…

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