Directions: Find the derivatives using the definition of limits (4-step Rule). Show each step from step 1 to 4. 6. y = (2x - 1)(7x + 3)

Q: 54. Determine the particular solution of the following differential equation: y'= 2yx Where: x=1;y=1…

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Q: 2. Consider lim 113 show of 9911 (99] uz to I He ai aidT MOTOR way to could orlob joylamaslo moy to…

A: I am attaching image so that you understand each and every step.

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A: See this solution in below.

Q: 3. lim tan x x→2/2

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Q: u.w= Perform the following operations on the vectors u = (-2, 1, 0), v = (-3, -5, -3), and w = (5,…

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Q: Suppose that the function f(x) 20.25 average molecular speed for this distribution? Write your…

A: Solution is given below:

Q: 30. Determine the particular solution of the following differential equation: 6y' = (2x + 1)(y² - 2y…

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Q: lowest term. Two cards are drawn in succession without replacement, in a deck of ordinary cards. If…

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Q: 11. g(x) = X, x-1, x < 0 x ≥0

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Q: 3. A semi-sphere tank of radius 7 m is full of water. How much work is needed to pump all of the…

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Q: Enter the exact answers. (a) Find the average rate of change of y = rave = with respect to x over…

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Q: How to 3x-2 gel 8x +4

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Q: lim x→1 x²+√x +2×-4 √√√x+3-2 h 58.11||||| find the value of (h)

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Q: 4. Evaluate the following and give the exact value: π/2 cosy -y π/6 0 'y sin(y+z) dz dx dy

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Q: Use the Vertical Line Test to determine whether the graph represents y as a function of x.   Yes,…

A: NOTE: Refresh your page if you can't see any equations. . if a vertical line intersects the graph…

Q: 7. Do Exercise 5 by another method. 8. Do Exercise 6 by another method.

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Q: Evaluate the difference quotient for the given function. Simplify your answer. f(x) = -x³, f(a+h) -…

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Q: 2) (y² co cos x - sin x) dx + (2y sin x + 2)dy = 0

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Q: 2. Evaluate the following and give the exact value: π/2 cos y are the (sin(y + 7) dz [** dx dy

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Q: xy dx - (x + 2y)² dy = 0.

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Q: * Evaluate (if possible) the six trigonometric functions of the real number. (If not possible, enter…

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Q: Find the solution of the following DE Show your complete solution 6. y² (1-x²)idy (arcsinx) dx :y(0)…

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Q: 4. lim tan-¹ 818 X

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Q: 16. (x-ylny + y lnx) dx + x(lny - Inx) dy = 0.

A: see below the answer and calculation

Q: What is the cardinal number of the set below? C = {Clemson, Colorado, Chico State, Columbia,…

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Q: If the tangent line to y = f(x) at (7, 3) passes through the point (0, 2), find f(7) and f'(7). f(7)…

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Q: 6₂. (W° x 5)-1

A: To simplify the following expression.w0x5-1

Q: Determine whether the given relation is an implicit solution to the given differential equation.…

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Q: Suppose you wish to retire at the age of 65 with $90,000 in savings. Determine your monthly payment…

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Q: A loan shark lends you $90 at 2% compound interest per week (this is a weekly, not an annual rate).…

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Q: 2x dy - y dx = x²y² dx

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Q: Differentiate the function: F(t)= (6x-5)2

A: Differentiate the function: F(t)= (6x-5)2

Q: Given that lim f(x) = 4 lim, g(x) = -5 lim h(x) = 0, find each limit, if it exists. (If an answer…

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Q: What is the angle in radians between the vectors a = (8, -1, -3) and b = (7, 7, -3)? Angle:…

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Q: 1. Use the graph of f(x) to find each of the following. a. lim f(x) = x-0 b. lim f(x): X→4- C. lim_…

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Q: Use the given conditions to write an equation for the line in point-slope form and in…

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Q: 8 3х

A: We have to simplify

Q: Show that f is continuous on (-infinity, +infinity) f(x)= { 1- x2 , if x less than or equal to 1…

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Q: Prove: २ tan² x sin²x = tan ²x -sin ²³ x ·

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Q: 775 775 878 909 940 946 Find, to the nearest unit, the mean solar intensity of the above data. 562…

A: Topic:- mean  Definition:- The mean (average) of a data set is found by adding all numbers in the…

Q: Solve (x − y + 3) dx − (x − y) dy = 0 ○ (x − y)² + 6x = C O (x - y)² - 4x +y = C O (x - y)² + 6x -…

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Q: Determine whether the following fun y = C₁x + ₂x³ + 2x²ex - 2xex is a solution to the differential…

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Q: Suppose z = f(u, v), where f(u, v), fu(u, v) and f(u, v) are differentiable functions of u and v.…

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Q: The graphs of y = f(z) (solid) and y = g(z) (dashed) are shown. The two graphs intersect at (7, 10).…

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Q: F(x) for f(x) is a function such that F'(x) = f(x). You might need to manipulate the function into a…

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Q: Find the average rate of change of the function f(x) = x² + 9x from x₁ =2 to x₂ = 5. The average…

A: As we know that; The average rate of change of the function fx between the interval x1≤x≤x2 is given…