Given f(x)=(1/3)x, for all the real values of x, use your GDC to find limx→∞f(x)lim.

Q: calculate the derivative of y with respect to x. express derivative in terms of x and y  e^6xy =…

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Q: Graph the set of points of continuity for the following function: f(x, y) = ln(-5x - 6y) 10 9 8 7 6…

A: The given function is

Q: A projectile's path is represented by the function h(t) = -4.9t² + 32t+4, where h is its height, in…

A: Average rate of change of f(x) on x=a and x=b is given by

Q: Write an equation for the transformed logarithm shown below, that passes through (3,0) and (-1,3) 3+…

A: To write an equation for the following transformed logarithm shown below, that passes through .

Q: 9. Find the interval of convergence and radius of convergence of the series n=1 2n (x - 1)n n

A: The objective of this question is to find the interval of convergence and radius of convergence of…

Q: Determine if the sequence is monotonic and also determine if it is bounded. a_n = ((2n+6)!) /…

A: The objective of this question is to determine if the given sequence is monotonic and if it is…

Q: If w = x + y²z, then the differential, dw is 0 1 + 2y 2ydxdydz dx + 2yzdy + y² dz 01+ 2yz + y² O dx…

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Q: A bicyde has a listed price of $572.98 before tax. If the sales tax rate is 9.75%, find the total…

A: Total Cost=Listed Price+(Listed Price×Sales Tax Rate)

Q: Let f(x) = 2x² + 13x + 15 -7x+5 2x² This function has: 1) A y intercept at the point 2) x intercepts…

A: Let To find the following: (1) y-intercept(s)(2) x-intercept(s)(3) vertical asymptote(3) horizontal…

Q: The key point (-12, 4) is on the graph y = f(x). What is its image point under the transformation g…

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Q: 4. When finding the derivative of a fraction you have to use the Product Rule. 5. The derivative of…

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Q: ilf find f'(x). Answer f(x) = 3 sin x 1 + cos a

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Q: Problem #2: Evaluate and determine whether the function is continuous at (0,0). Provide…

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Q: Find the equation of the tangent line to y = 7e* at x = 8. (Use symbolic notation and fractions…

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Q: 1. Consider this series: 10 20 3 9 (a) Write the series using sigma notation. 5+ + 40 80 27 81 + ()…

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Q: What is v'(5)?

A: The objective of this question is to find the derivative of the function v(x) = f(x) - 2g(x) at x =…

Q: Calculus 2 Let A E RNXN be a symmetric, positive definite matrix and b E RN a vector. If x ERN,…

A: The integral Z(A, b) as a function of A and b is given by: Z(A,b)=e21​bTA−1b(2Π)Ndet(A−1)​ This…

Q: numbers, mathematics unveils the poetry hidden in every calculation, revealing the elegant…

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Q: Evaluate the following integral. 48x² S (x - 15)(x + 5)² 48x² (x − 15)(x + 5)² √ S. dx dx = 48 7…

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Q: The upper half of the ellipse centered at the origin with axes of length 2a and 2b is described by b…

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Q: a. Σ=zk2 b. Σ=1(1 + j)3 (1+j)³

A: To re-write the sigma notation as a summation and to perform the indicated addition.

Q: Please solve

A: A.     limx→3−​f(x)=1Explanation: Notice that as x approaches 3 from the left, y approaches 1.…

Q: -5 -4 -3 fa 4 3 2 -3 O 2 3 4 10

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Q: Heron's formula for the area A of a triangle with sides of length a, b, c > 0 is A = √√√√s(s − a)(s…

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Q: Differentiate the following function: ƒ'(x) = f(x) = ex + x²

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Q: ƒ' (4) = If f(x) = 3√√√x(x³ − 2√x + 2), find f'(4).

A: Given that

Q: Find the difference quotient f(x) = f(2) x-2 when f(x) = 4 - 5x + 5x². Simplify the expression fully…

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Q: a. lxldx b. (1+x1) dx

A: To sketch the graph of the integrand function and by using it to evaluate the integral.

Q: -) y = 7sec @ In 7 ) y = 5-cos 2t 5) y = 3tan@ In 3

A: Since there are two different questions, according to the guidelines, I am solving the first…

Q: (BC Topic) Which of the following statements about the series below is true? (-1)" Ž n=11+√√n²³…

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Q: Please help evaluate

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Q: cos3tdt d. tantdt

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Q: Find f'(x), f(x), and f'(x) for the following function. f(x)=2x +5ex f'(x) = f''(x) = f''(x) =

A: The given function is   .The objective is to find f'(x), f''(x) and f'''(x) .

Q: 1. Use the definition to compute the exact average Show all details of the integration process. a b…

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Q: Find the centroid of the region lying underneath the graph of the function f(x)=√ over the interval…

A: f(x) =

Q: Use the accompanying sections of a table of integrals to evaluate the following indefinite integral.…

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Q: Let f(t) = 3t2/3 + 5/3 (a) Find all partition numbers of f'(t). (Enter your answers as a…

A: Note:As per our guidelines we are supposed to answer only first 3 subparts if there are multiple…

Q: 9. Evaluate the limit for the graph: lim f(x). x → 0 a. b. y 4 2 11 20 2 does not exist +00 4 x c. 0…

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Q: ) Determine the vector function r(t) that describes the curve of intersection between f(x, y) and…

A: The given function equation is

Q: Find the limit of the sequence as n approaches infinity: 2n 9 In +8 an www

A: The given nth term of sequence is

Q: 1. We're going to use the Ratio Test to figure out whether the series An= (a) First, write…

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Q: 2. Sketch the graph of f(x) = 3x3/2. Highlight the graph over the interval [2,3]. Now find the arc…

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Q: If f'(x) = 10x⁹, what is f(x)? (Remember the constant of integration.) f(x) = X

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Q: Suppose f (0) = -6 and f'(x) ≤ 8 for all values of x. How large can f (-3) possible be? (use the…

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Q: Find the derivative of the position vector r(t) = -eti +(t – t²)j +In(t)k Find the tangent vector at…

A: Given: To Find: (i) To find the derivative of the position vector.(ii) To find the tangent vector at…

Q: Evaluate the following integral using trigonometric substitution.. 9 S 8 dx x²√64x²-81 2 dx…

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Q: Suppose that f(x) = (x + 2)(x - 2)². (a) Find all critical values of f(x). (Enter your answers as a…

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Q: cond partial derivatives. Observe that the second mixed partials are equal 4xey - 5ye-x X X

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Q: x Y Suppose w = + where Z Y x = t, y = 2 + sin (4t), and z = 2 + cos (3t). A) Use the chain rule to…

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Q: Determine the slope of the tangent line to f(x) = 3x-2 x²+4x at (-2, 2).

A: f(x)=3x−2x2+4x at (−2,2).Quotient Ruleddx[f(x)g(x)]=g(x)f′(x)−f(x)g′(x)[g(x)]2