1. Use the precise definition of a limit to show that 12 lim x-3-x-3 8

Q: Use finite approximation to estimate the area under the graph of f(x) = 6x² and above the graph of…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Find the derivative of the function. f'(x) = f(x) = (x³ - 4x)(2x² + 3x)

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Q: Use the method for solving equations with linear coefficients to solve the following differential…

A: The given differential equation is:(2x-y)dx+(4x+y-3)dy=0

Q: Find the length of the equiangular spiral r = (Use symbolic notation and fractions where needed.) 5e…

A: To find the length of the equiangular spiral r=5eθ for 0≤θ≤2π.

Q: Solve the equation. (4x³ + 3x¹y)dx + (x³y-1)dy=0 An implicit solution in the form F(x,y) = C is =C,…

A: We use the techniques of exact differential equations to find the general solution of given…

Q: Find the indicated limit. lim (8t2 - 7t + 1) t-6

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Q: Determine all the singular points of the given differential equation. (t²-t-12) x + (t+3)x' -…

A: Let a differential equation be like        p(x) y'' + q(x) y' + r(x) y = 0 Then we can write it as…

Q: d²y at the given value of t to the curve defined below dx² x = t - sint, y = 1-cost, t = 3 Find the…

A: x=t-sint y=1-cost Differentiating x with respect to t  x't=dxdt dxdt=ddtt-ddtsint dxdt=1-cost…

Q: A can in the shape of a right circular cylinder is required to have a volume of 500 cubic…

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Q: Evaluate the limit. lim √-2x +3 x-4 O-2√19

A: Given expression of limit  limx→-4-2x+3

Q: Find the volume of a parallelepiped with the given vectors as adjacent edges. u=(-9,-3,-4> V= w=

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Q: Find the sum of the geometric series. −3 – 12 – 48 – 192, ... n = 6 O -3692 O -3320 0 1 O-4095

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Q: Find the first and second derivatives of the function. f'(x) f"(x) = L √7x - 6

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Q: Evaluate the limit. lim x→0 O-1 05 07 09 1 -1+x X +1

A: To evaluate the following limit. limx→0 1-1+x+1x

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: o Find the polar equation of a line parallel to the line r cos (0 - (Use symbolic notation and…

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Q: Sketch the region enclosed by y = 5x and 9x². Find the area of the region. y =

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Q: find the point y=5x origin + 2 that js on the line closest to the

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Q: A can in the shape of a right circular cylinder is required to have a volume of 500 cubic…

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Q: Write the vector as a linear combination.   RS where R=(-4,-5) S=(1,5)

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Q: dy 1) (a) Find the equation that satisfies the following IVP: =.5y_y(0) = 20 dx (b) Find the IVP…

A: To find out the particular solution of the given differential equation.

Q: Use the graph of the function f to solve the inequality. (a) f(x) > 0 (b) f(x) ≤0 (a) The solution…

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Q: Solve the inequality algebraically. x3³ -5x² - 6x>0 List the intervals and sign in each interval.…

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Q: 9. A demand curve is given by D(x) consumer surplus CS if p = $800. x-8 Compute the

A: The demand curve is given by Dx=450x-8

Q: Question 17 Solve the equation for all solutions in the interval 0≤ t < 2π. Give your answers as…

A: sin(π + x) = -sinx sin(π - x) =  sinx

Q: Graph  f(x) = ax  for  a =  1 3,   a = 1,  and  a = 3,  all on the same set of axes.

A: Given: f(x)=ax We are required to: Draw the graph of the given function for a=13,a=1 and a=3.

Q: Solve the inequality algebraically. 3x³>- 12x² List the intervals and sign in each interval.…

A: Given: 3x3&gt;-12x2 We are required to find: The solution of the given inequality.

Q: Determine dy dx if y = √³ - e²¹ and x = 3t In(5t)

A: To determine dydx if y=t3-e2t and x=3tln5t.

Q: 1. Find the first line ONLY of the derivative showing the product rule. a) y = (- 2x¹ + 2x³ - 8)…

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Q: For the function f(x) = ax³ + bx²2, find a and b so that the point (1,6) is an inflection point of…

A: The function is given as , fx=ax3+bx2 find a and b so that point 1,6 is an inflection point of f.

Q: 7 Given the complex number 2₁ = 30√2(cos+ i sin ) and 22 = 5(cos+isin), express the result of 21 in…

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Q: Q3 Sketch and evaluate ²x²dx

A: 3) Given that ∫12x2dx

Q: (6) (a) Use three conditions of continuity to show that f(x)=√ is continuous over (7, ∞0). (b) What…

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Q: Use a double integral in polar coordinates to find the area A of the shaded region shown below. A-…

A: When we established the double integral for a continuous function expressed in rectangular…

Q: 8. Suppose that the position of a particle at time t is given by c(t) = (2t - 1, t³/2). Compute the…

A: Suppose that the position of a particle at time t is given by  ct=2t-1, t32. To compute the distance…

Q: Find the length of spiral x=40² 2 48 03826 Lev. 40² 2 ² + (²) ² de

A: r = 4θ2Length = L L = ∫ab[ r2 +( r' )2]dθ0 ≤ θ ≤ 6

Q: 225 ft X A building that is 225 feet tall casts a shadow of various lengths as the day goes by. An…

A: given x=209

Q: cos Replace the polar equation r= (csc 04 The equivalent Cartesian equation is y=[ Choose the…

A: We need to find cartesian equation and draw graph.

Q: Determine the inverse Laplace transform of the function below. 5s Se s²+2s+17 Click here to view the…

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Q: 1) Evaluate the integral using area formulas: (first draw the region) 1²₂ √4 - x² dx

A: ∫-224-x2dx

Q: Consider f(x) = ax3 + x + 1, where a is a real-valued parameter. Find all possible values of a such…

A: The function is given by  fx=ax3+x+1  Maximum value ÷ 43 Minimum value ÷ 23

Q: 12) Use Part 1 of the Fundamental Theorem of Calculus to find the derivative g'(x) of the given…

A: gx=∫5x2t3+74dtTo find : Use Part 1 of the Fundamental Theorem of Calculus to find the…

Q: Use linear approximation, i.e. the tangent line, to approximate 8.4 as follows: Let ƒ(x) = √ï. The…

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Q: Solve the following IVP: f'(x) = 4x - 1 given f(2)= 5

A: Given: f'(x)=4x-1, f(2)=5 We are required to: Solve the given differential equation.

Q: b) Use the Mean Value Theorem to show that sin x 0.

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Suppose you use a tracking telescope to follow a rocket. Suppose you are also 2000 meters from the…

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Q: Determine whether the sories Σ ma converges or diverges. If it converges, find its sum. Select the…

A: The given series is: ∑m=2∞ 74m

Q: 1. S dx √4-x

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Q: Using the definition, find the derivative of f(x) = _I 3√x -X

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Q: The function f(x) f(x) = [ n=0 J C2 C3 Find the first few coefficients in the power series. Co = C4…

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