Find the first three terms of the Taylor series in x - a. ex. a=3

Q: Suppose 4²x = 12. Then x = A. In12 OB. (√12)³ 3 OC. 3 D. 109412 E. 09122 2

A: 1). logbxa=a·logbx  where x,b>0, b≠1 2). logbb=1

Q: 3. Differentiate the following exponential function without simplifying f(x)=√(e*)(2x)

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Q: A line has y-intercept 11 and z-intercept –13. Find a vector equation of the line. O A) [x, y, z] =…

A: The line has y-intercept 11 and z-intercept -13. So the line passes through points A(0,11,0) and…

Q: Find a series expansion centered at x = 0 for M8 Σ • Sf² 2²², n=0 t¹³ sin(t)dt.

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Q: 2. For each problem, find the length of the curve. (a) y = (e+ e-*) on the closed interval 0 ≤ x ≤…

A: Solving the problem

Q: 1. Solve the following DE using Variation of Parameters: (D2 + 1) y = secx tanx

A: given that (D2+1)y=secx tanx solve it by using method of variation of parameters

Q: 3. A paper cup has the shape of a cone with height 15 cm and radius 5 cm (at the top). If water is…

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Q: T -2 4 f(x) g(r)|h(r) 5 4 9 2 -3

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Q: Evaluate the given definite integral. -23 125 th In x

A: let D=∫123lnxxdx

Q: Solve the following differential equations dy dr² dy -9x+24y=0, y(1)= 1,y(1) = 0 dx

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Q: Find the parametric and symmetric equations for the line passing through the point P(1,-3,6) and it…

A: Equation of the line passing through the one  point and parallel to the given line

Q: What is the volume of the 3D region obtained by rotating the following 2D region around the y-axis…

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Q: Fill in the missing entries of the matrix, assuming that the equation holds for all values of the…

A: Two matrices are said to be equal if they have the same order and the corresponding elements are…

Q: Suppose a company has fixed costs of $400 and variable costs per unit of x + 1350 dollars, where x…

A: Suppose a company has fixed costs of $400 and variable cost per unit of  1516x+1350 dollars, where x…

Q: Sketch a graph of the function f(x) = 3sin x. Please state the range.

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Q: Michelle invests in a savings account that pays 8% interest compounded monthly. What is the APY for…

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Q: 2. Differentiate the following functions a. f(x) = 12²x - x² 2 b. f(x) = (e²x-3) + x c. f(x)=…

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Q: forin the egral. ayus 4. Perform the line integral for 0 ≤ t ≤ 1. where the cur is the straight me…

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Q: 8. For f(x, y) == xex²y Find fx (1, 2) {needs product rule}

A: Explanation and some important formulas:

Q: What is an antiderivative of the function x + 2xln(x)? x²ln(x)+2023 xln(x) +2023 In(x) + x xsin(x) +…

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Q: Q6 Use the graphs below to fill in blank. Write DNE" for Does Not Exist" or NEI" for Not Enough…

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Q: What is the reference angle of θ if θ = –137°? A 43° B 47° C 137° D 223°

A: Explanation of the answer is as follows

Q: Complete the computations in Exercises 5-8. 5. (6,0, 5) + (5,0, 6) = 6. (0,0,0) + (0,0,0) = 7. (1,…

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Q: y"" + 25y' = 0

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Q: If a company has total costs C(x) = 40,000+ 15x + 0.2x2 and total revenues given by R(x) = 595x…

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Q: 1. let y = x(x2+x)2  , Find y'   2. let f(x) = (5x)5 find f '(x)…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: A CD has diameter of 130 millimeters. When playing audio, the angular speed varies to keep the…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

A: Given that a a functio f(x, y) = x2 +xy + y2 +2y. And we find local maximum value and local minimum…

Q: 3. Consider the following vectors: (2,3) & (-5,1) a. Find the dot product between them b. Find the…

A: We have to find the dot product and angle between two vectors.

Q: Find the intercepts and the vertical asymptote of Enter the intercepts as points, (a, b). The…

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Q: A plant with a mass of 10 kg is suspended from a ceiling by two lengths of rope that makes angles…

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Q: The vector k represents: O A vector of manitude 1000 in any direction. O A vector of magnitude one…

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Q: Use the equation to find dy dx dy dx || | OF дх OF ду || | ㅠㅠ X 3ey sin(x) = x + xy

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Q: The complete graph of y = f(x) is given below. Use it to graph the following function. g(x) = f(x) +…

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Q: Given one form a line, match it with its equivalent equation in another form. = 0 { y = 1 Z=t 1. 2.…

A: We are given a line in 3d space  x=0 y=1 z=t We are to find the general equation of the given line

Q: The region R in the first quadrant is bounded by the coordinate axes, the curve y=e -5x The (exact)…

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Q: ₁²√3x²2dx, u = 3x² - 2 du

A: Use the u-subsituation

Q: 1/3 The integral fo²³ 3-√2-9x1² dx is to be evaluated 0 directly and using series approximation. 1)…

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Q: The owner of a skating rink rents the rink for parties at $1000 if 50 or fewer skaters attend, so…

A: Note: Due to Bartleby policy i can solve only the first question with its 3 subparts.     The cost…

Q: Suppose that lim an = 5 and lim bn = 9. n-0 n→∞ Determine the limits. lim (an + bn) = n→∞o lim a =…

A: We are given that limn→∞an=5 and limn→∞bn=9.We need to find the given limits.

Q: Let f(x)= - (2.-17). a. Use the following definition of the slope of the tangent line at x = a to…

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Q: 4. Determine the values of a and b such as the two vectors (2,1, a) & (b,-2,2) are a. Perpendicular…

A: We hae to find the vales of a and b for the given conditions.

Q: One side of a triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate…

A: One side of a triangle is increasing at a rate of 9 cm/s and a second side is  decreasing at a rate…

Q: Perform the indicated integration using INTEGRATION BY PARTS 1. √z. In z dz

A: To perform the indicated integration by using integration by parts. ∫z·lnz dz Note: Since the…

Q: Given the function f and the point Q, find all points P on the graph of f such that the line tangent…

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Q: Evaluate the integral. π/2 [" os⁹(x) sin5(x) dx

A: NOTE: Refresh your page if you can't see any equations. . use the formula  ................(1)…

Q: Evaluate the given definite integral. 6 x√x-6 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) [tan²(x) cos³(x) dx

A: let B=∫tan2xcos3xdx

Q: a = (-2,4), b = (-1,2), what's the projection of a on b?

A: We know that the formula projection of A on B is  (A.B)/|B|

Q: 6. Suppose that a. 6 b. 2 a b - 3c = 0 → → and a c= 2. What is a C. -6 d. -2 → b equal to?

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