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Q: 2x² + 1 Find the lim, f(x) where f(x) : if xs -5 x – 3x-2 if x > -5 x-5* -122/25 O -72/25 O -80 None…

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Q: Let the region R be the area enclosed by the function f(x) = Va and g(x) = x. Write an integral in…

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(1,…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Assume that C(x) is in dollars and x is the number of units produced and sold. For the total-cost…

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Q: (a) How far is the boat from the marina? Round the answer to one decimal place if necessary. (b)…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: e" + e¯ cosh(r) : e - e sinh(r) 2 Use our rules for differentiating e" to show that cosh'(r) =…

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Q: Find the orthogonal trajectory for the family of straight lines passing through (3,-5).

A: Find your answer below

Q: Differentiate implicitly to find dy/ dx. Then find the slope of the curve at the given point. x²y? =…

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Q: |(sinx/cos2x)dx = sec x + C %3D Select one; O True O False 16x e2^3+1 dx = 3e3+1 + C Select one…

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Q: After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world…

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

Q: Find the limit. lim V+3

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

Q: Suppose that enrolment in CLSU has been increasing over the years since year 2013 according to the…

A: Given query is to find the enroy in 2022.

Q: with A parti cle is moving a cc eleratoN at) = 12t+18. Its positian at time t = 0 IS S© =4 and its…

A: This question is related to integration, we will solve it using given information.

Q: Find the open intervals on which the function is increasing or decreasing. Apply the First…

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Q: Example 2 Compute (a) (1+i)/(3-i) and (b) (1+i)4.

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Q: 'ind the exact length of the curve x = t sint y = t cos t or 0<t< 1. ou may use the following result…

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Q: Find the dimensions of a rectangle with area 216 m² whose perimeter is as small as possible. (If…

A: Find your answer below

Q: Solve for t. log 6 t= 2

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

Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: E Homework: Section 4.7 Use the given zero to find the remaining zeros of the function. h(x) = x -…

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Q: V25x² -69 – dx

A: We will find the integral as following.

Q: Use the cylindrical shell method to calculate the volume of the solid formed by rotating the graph…

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Q: Suppose the position of a particle is given by parametric equations x(t) = t³-2 and y(t) = 5t2. %3D…

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: Consider the function y = 5cos(x). What are the exact values of C in the interval [0, 2pi] such that…

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Q: EXERCISES write the number in the form a + jb. (a) – 31 (b) (8 + j) – (5 +i)

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Q: 2. Solve the given the equation using the integrating factors found by inspection. [2х + усos(ху)jdx…

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Q: (sec3x The integral of the given function f (sec dx is \tan3x. cot³3x cot3x + C 3 а. 9 cot3x cot3x…

A: cot2x+1=csc2x sec(x)tan(x)=csc(x) ddx(cotx)=-csc2x ∫xndx=x(n+1)n+1, for any real number n.

Q: If a cylinder, a hemisphere and a cone stand on equal bases and have the same heights, what will be…

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Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: Solution :let, side of square=xArea of square=Adxdt= 8 cm/secA= 36 sq. cmA=x2    Area of square=side…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 5, -1) Vw(9, 5, -1) =

A: Explained below

Q: 1-. 5x <35 -2 (х-3) (х+3)* (*+1(5-х) 7-3. 2х - 3 <4 x-1 2.4, 25. -23х -5 - 8<-20

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Q: Using Integration by parts, evaluate: ſ x³Vx³ + 1dx Your answer

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Q: For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is…

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Q: The sum of two positive numbers is 20. Find the product of the two numbers if the sum of their…

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

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Q: Find a positive number such that the sum of the number and its reciprocal is as small as possible

A: Second Derivative Test :   Firstly find critical point of f(x).i.e, f'(x)=0 and find the value of…

Q: A 400-lb cable is 250 feet long and hangs vertically from the top of a building. How much work is…

A: A 400-lb cable is 250 feet long and hangs vertically from the top of a building. ρ=mass per unit…

Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Given the graph of the function below. Find the limit of the functic approaches 3.* (3, 4) (0,3)…

A: Given query is to find indicated limit.

Q: x² – 16 Evaluate lim x4 2- Vx O -32 None of these 1 O 32 O does not exist

A: Given  Lt   x²-16/(2- √x)        x-&gt;4

Q: A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting…

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Q: Let the region R be the area enclosed by the function f (x) = e® + 2 and g(x) = 6x + 3. Write an…

A: Given: f(x) = ex +2,    g(x)=6x+3

Q: given point 1. y = 2x° - 3x² - 2x + 5 ; where x 1

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

Q: Use the gradient to find the directional derivative of the function at P in the direction of v. g(a,…

A: Let's find.

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: We have to find the increase of area