Find the value of the given limit. lim I 0 tan(4x) I

Q: What is the slope of the line represented by the following formula? y = 2 + 6(x - 3)

A: Given,            y=2+6x-3To find : What is the slope of the line represented by the following…

Q: Evaluate: fre Hint: Use dyda as order of integration. ezz drdy

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors 1² +2 x² +2…

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Q: Find and sketch the domain of f(x,y)=√1-(x + 1)² - y² + 2ln(x -y + 1)

A: Let's find domain of given function.

Q: Onsider the function f(x) = -4x²+7x+6. Interpret the e average rate of change from x = -7 to x = 7…

A: Topic:- application of calculus        Definition :-  The tangent represents the instantaneous rate…

Q: A function is given. Determine the average rate of change of the function between the given values…

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Q: e Find the volume generated by revolving the area enclosed by the loop of the curve y² = x (x-3)²…

A: Solution is given below:

Q: Consider the integral (ln(x))6 dx:

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Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

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Q: The x value(s) of the point(s) where the tangent line(s) to the curve y = ³ - 6x that have a slope…

A: Here we have to find the value of x.

Q: Use the rules for sums of powers of integers to compute the sum. 22 [² j=8

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Q: : x-2y+3z-1 = 0 and the line 1 : x = Consider the plane 1. Find the point of intersection of and 1.…

A: Given: x-2y+3z-1=0x=1-y2=z+1

Q: . Let f be a function of two variables such that and f(2, 1) = 4. af Ət If, in addition, x = r cost…

A: The given gradient of the scalar function fx,y is ∇→fx, y=3x2-3y, -3x+3y2. Also, we have f2,1=4.…

Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

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Q: S 1 (x²+6x+5)3/2 dx

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Q: A particle is moving with acceleration a(t) = 6t+ 6. its position at time t = 0 is s(0) = 11 and its…

A: GIven: a(t)=6t+6 s(0)=11 v(0)=9   We know that, the integral of acceleration with respect to time…

Q: Use integration by parts to find the antiderivative of f(x) = ln(x).

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Q: 8 №₁ 4-x² x+4.x² dx

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Q: ) Use the Product Rule or Quotient Rule to find the derivative of f(x) Do not simplify. O f'(x) = O…

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Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

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Q: Find the arc length of the following curve on the given interval by integrating with respect to x. y…

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Q: 7. Solve for cot 0 (² - if cos(20) = 4 5 and P(0) E QIV.

A: To solve for cotθ2 if cos2θ=-45 and Pθ∈QIV.

Q: Given the function graphed below, evaluate the definite integrals. -1 4 3 2 1 1 -1 -2 -3 -4+ […

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Q: 2. Find the general / particular solution of the following using variable separable b. mydx = nxdy =…

A: Given: a)  my dx=nx dy       separable equation:        mxdx=nydy integrate on both sides…

Q: CALCULATE THE AREA BETWEEN THE GIVEN FUNCTIONS. DEVELOP THE PROBLEM WITH ALL STEP EXPLAINED AND…

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Q: 2 y²dx + xydy = 0

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Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: O

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Q: 5 S³ƒ( en that wer= f(x)dx 10 3 is ['f f(r)dr? what is

A: Topic :- application of integration

Q: 7. A jar contains black and white marbles. Two marbles are chosen without replacement. The…

A: Solution is given below

Q: Find the total surface area and volume of the solid object shown to the right. Use the key for s The…

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Q: This exercise uses the radioactive decay model. The burial cloth of an Egyptian mummy is estimated…

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Q: Consider the function f(t) = 3 sec²(t) - 3t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: 뿐 for the following: y = ln(e2z) 0 읊 ○ 2 Oezz ○ ez (In 2)

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Q: 1 cot³ x dx =

A: To solve the given integral.

Q: Given f''(x) = - 36 sin(6x) and f'(0) = 6 and f(0) = 0. Find f(1) = [

A: Given the function f''x=-36 sin6x and f'0=6 and f0=0 use the integration formulas,…

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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Q: •+∞0 4-1² 1 x² + 4x² dx

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Q: Q2:A: Find the surface area of the cone y = h -√x² + z² where h is the height of the cone and a is…

A: Concept: The surface area of the cone: The total area that a cone's two surfaces, its circular base…

Q: Use mathematical induction to prove that the statement for all positive integers. + (2n-1) = n² a)…

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Q: The linear density of a rod 3m long at a point x meters from one end is ke-3x kilograms per meter.…

A: Solution is given below:

Q: D Question 20 Use Euler's Formula to express 5ie in a form of a + bi. O + 1 2 O 5√3 5 + 2 O 5√3 2 2…

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Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: Given,           Rx=7x and Cx=160-2x+x2To find : How many pizzas sold maximizes the profit.

Q: 1 ∞ Inxdr

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Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

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Q: 5. S (2x²-3x+10)dx (x²+4)²

A: I have stated the used formulas in the solution

Q: Viola makes gift baskets for Valentine's Day. She has 12 baskets left over from last year, and she…

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Q: Wants to know what will be the Maclaren series of g(x) = sin(x) is ?

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0…

Q: The marginal revenue from the sale of x cans of air freshener is given by 4.4 -0.32√x dollars per…

A: In here, the marginal revenue is given as a function of x. So, we will use the formula: Marginal…

Q: Given f(x) = 2* cos x, 0 ≤ x ≤ í, find the critical point(s) on the given interval. If necessary,…

A: Answer :   Critical point : x = 0.193π and increasing in nature.