Consider the ellipse r(t) = 2 cos(t)i + sin(t)j. (a) Calculate the unit tangent vector and unit normal vector. (b) Express the acceleration in terms of the tangential and normal components.

Q: 3 The function f(x) = 2x³ 2x³ 21x² + 36x - 8 has two critical numbers. The smaller one is x = and…

A: Given, .For find critical numbers put f'(x)=0.

Q: Let C be the curve defined by x = e¹, y = 10 - et for 0 ≤ t ≤ 2. Evaluate each of _ds, [ -= ds.…

A: Given that let C be the curve defined by for To find:-

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A: (a) given, if

Q: True or false: If f is differentiable at a, then it is necessarily true that f(a+h)-f(a) h f'(a) =…

A:

Q: Test the series below for convergence using the Ratio Test. Ë n=1 3n n! The limit of the ratio test…

A: The power series is given byCriteria of Ratio TestIf 1, The series diverges end text text L

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: f(x) = 1/5 - 9/x             ,x>0

Q: Test the series below for convergence using the Root Test. 8n² 8 n=1 6n + 4 4) f(n)= The limit of…

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Q: 3 5, x < 15. f(x) = {_x²+3, X2-1² -2x If f is the function defined above, then f'(-1) is?

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Q: 1) Find the general solution of the following differential equation y" - 6y +9y = 0

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Q: The velocity of an object is shown in the graph below 5+ 4 Velocity (m/s) N لا 3 1 1 pasij 3 Time…

A: The velocity of an object is shown in the graph below.To calculate the total distance traveled over…

Q: Let lim g(x) = -1 and lim h(x) = 10 x 4 x→4 Determine the value of the limit lim [8+√xh(x) x→4

A: Let, To determine the value of the following limit.

Q: Use Trigonometric Substitutions to evaluate the integral. S= x² √1-x² dx TA

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Q: +∞ Σ n=1 Determine whether the series is a convergent or divergent 1 nn -2

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: The expression of the derivative of the function  is given by The point is To determine: The…

Q: Find the arc length of the curve on the given interval. Interval Parametric Equations x = 7t + 5, y…

A:

Q: Ox-2y=0

A: Given that the graph we have to find the equation of tangent line at the point origin

Q: Let f be a differentiable function such that ƒ (3) = 15, ƒ (6) = 3, ƒ′ (3) = −8, and f' (6) = -2.The…

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Q: K Find the area of the region bounded by the graphs of the given equations. y=x² +6, y=x², x= -3,x=2…

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Q: Find f'(x). f(x)=(7x+4)(9x-3) f'(x)= (Type an exact answer.)

A: Given, .Rules of derivative:

Q: m 4. Consider sin x cos" xdx. (a) How do you evaluate fsin" x cos" xdx if m is odd? (b) What if n is…

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Q: 2. d²y dx² dy dx +9y=0.

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Q: Write the sum without sigma notation. Then evaluate the sum. 2 Σ k=1 12k k+ 2 Write the sum without…

A: The given sequence is

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A:

Q: Compute the mean, median, and mode of the data sample. (If every number of the set is a solution,…

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Q: Find the derivative of f (x) = ln O f'(x) © f'(x) O f'(x) O f'(x) = = = = | 8 + sin x f (x) = ln (…

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Q: Consider the following parametric curve. Answer parts a and b. 64 dx x = 4t+y=4t-t=4 a. Determine in…

A: The given parametric curve equation is

Q: Evaluate the following determinant. Show all steps 2 1 -1 1 3 0 -2 2 4

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Q: ind an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (5,…

A: Given that the point (0,0,0) ,(5,0,7) and (-4,-1,4) we have to find the equation of the plane…

Q: For the given cost function C(x) = 44100 + 700x + x², First, find the average cost function. Use it…

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Q: A company determined that the marginal cost, C'(x) of producing the xth unit of a product is given…

A: Consider the given marginal cost function.C(x) is the cost function and the fixed cost is $3000.

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

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Q: The polynomial of degree 4, P(z) has a root of multiplicity 2 at = 3 and roots of multiplicity 1 at…

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Q: Suppose that the profit of a company depends on three variables (x,y,z) and is given by the equation…

A:

Q: 4

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Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = -2…

A: To find the intervals on which  is increasing and decreasing.

Q: 13. If f(x) L x-1 x #1 4, x = 1 lim f(x) exists which of these statements are true? II. fis…

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Q: If tan0 = 11/9 and cos 0 > 0, then without finding the angle, find the exact answers to the…

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Q: Find the absolute maximum and minimum y-values of f(x) = x - 4 In(x) on the interval decimal…

A: Consider the function

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Q: 3 The function f(x) = √(x − 1)² does not satisfy the conditions of the Mean Value Theorem on the…

A:

Q: Write a triple integral, including limits of integration, that gives the volume between 3x +2y + z =…

A: The given equation are 3x + 2y + z = 35x + 3y + z = 3x + y  1, x  0, y 0

Q: Let g(x) = f(t) dt where fis the function whose graph is shown in the figure. y f LA t 1 2 3 4 5 6 7…

A:

Q: If ƒ(x) = 3x² – 3eª, find:

A: f(x)=3x2−3ex

Q: A toy company is trying to determine the optimal price for their weekly supply to meet the demand…

A: The objective of this question is to determine whether there will be a shortage or surplus of toys…

Q: 8. Evaluate the following limits: 1 (a) lim xx x r (- − arctanr) (b) lim x² xxx

A: Here we will find the limit of the given functions on using l hospital rule

Q: 2x Use the function f(x) x² + 5 (a) Find the interval(s) on which f(x) is increasing. Number of…

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Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

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Q: A ball dropped from a height of 14 feet begins to bounce. Each time it strikes the ground, it…

A:

Q: Differentiate the following function. f(x)=9-4x+5ex f'(x) =

A: Given,

Q: Consider the indefinite integral 152³ The integrand has partial fractions decomposition a b cx + d…

A: