Determine the limits of: 3N (1 + 2/3 3³

Q: Express the given equation into the exponential form and then solve for x. log2 (5x - 10) = 3

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Q: Compute the derivative of the following function. f(x) = 5xe-5x f'(x) =

A: we need to find out the derivative of the given function.

Q: Compute the Taylor polynomial of degree 4 for g(x)=cos x centered at x=0.

A: To compute the Taylor polynomial of degree 4 for  centered at .

Q: Evaluate the following integral 8 ["* e* dx е 0

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Q: How do I prove, |3- x/3| 9 (1 - x/3x)=-2

A: If is a function and then we say  if for any  there is  such that .

Q: 4. A = [ 5 7 5 ²]. b = = ['₁ 5 12 17

A: Given,

Q: A particle moves according to a law of motion s= = tª — 2t² + 1, t > 0, where t is measured in…

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Q: f(x) = 3x²/3-x on [0,27]

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: We have to find the absolute maximum and minimum values of the function over the indicated interval,…

Q: Differentiate d dx y = 11x4 + 3 - (1₁x² + 3) =

A: As we know that

Q: Consider a trapezoid that has a constant area of 300 cm. The height of the trapezoid is increasing…

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Q: Find dy clx In (sin(8x3)) a) y=(√√x2-1) In (sin( b) y = 1+ sin ² (3x)+sin 4 (3x) + sin 6 (3x)+.... +…

A: Since, you have posted multiple questions.As per guidelines we are supposed to answer only first…

Q: 3. Solve the following homogeneous differential equations a. y"-4y'+4y=0

A: To solve the following homogeneous differential equation.Note: Since the student has posted multiple…

Q: Find the area of the surface. The portion of the plane z = 6 - 3x - 2y in the first octant 6√14

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Q: Nû 4 - x X X dx

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Q: (m) (ex)= = (0) dx dx (logax) = (n) (lnx): dx = (p) & (a*) = dx

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Q: 2 y³ 4. Solve y' +-y X X² = using the following technique: A Bernoulli differential equation (named…

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Q: Find the present value of $2000 payable at the end of 3 years, if money may be invested at 4% with…

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Q: Find the logarithm using the change of base formula. log 717 log717= (Round to four decimal places…

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Q: Let f(x) = In(x). State if the following statement is true or false (a) The graph of f(x) has a…

A: According to bartleby guidelines we are supposed to do only one question.  If you want more to be…

Q: Find three positive numbers whose sum is 160 and whose product is a maximum.

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Q: 7x 1+2x 2+1 x_3+8 x_4+9x_5 = 69 9x 2+3 x 3+4x_4+4 x 5 = 54 4x 1 + 6 x 2+5 x_4+4 x 5 = 40 2x 1 + 10 x…

A: We solve the following system of linear equations using the Gauss-Jordan Elimination Method:

Q: Find the eigenvalue associated with the eigenvector A = Number -[-28] = of the matrix A=

A: The given eigenvector is The given matrix is

Q: Use the Chain Rule to find dz dt 1 where z = 3x siny, x = t², and y = 2t4.

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Q: 5. §11.5. Q31. Use a chain rule to find the value of dw dxs=1/4 if wr² - rtan 0, r = √s, 0 = πs.

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Q: The function f(x) = −2x³ – 19.08x² +70.179x - 3.59 is increasing on the open interval ( ). It is…

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Q: Write an equation for a line perpendicular to y = 5x - 4 and passing through the point (10,-7) y=

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Q: If a snowball melts so that its surface aree decreases at a rate of 10 cm2/min, find the rate (in…

A: Shape of snowball is sphere.

Q: Find dy dy dx by implicit differentiation. tan(x - y) = = y 7+x²

A: Here to find implicit differentiation , we must differentiate both sides of the simplified form of…

Q: Write a fraction to represent the shaded portion. Need Help? Read It

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Q: 1. Change the equation x² + y² + 6x - 16 = 0 to standard form and determine the coordinates of the…

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Q: Use the arc length formula to find the length of the curve y = 7 − 4x, −1 ≤ x ≤ 2. Check your…

A: For a function  , The arc length from is given as follows

Q: 2. Find a function f such that f'(x)= xf(x)-x and f(0) = 2.

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Q: Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros…

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Q: 4. A suspension bridge with weight uniformly distributed along its length has twin towers that…

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Q: -4-3 4 3 2 1 -1- -2 -3- 1 f(x) 2 3 X g(x) 4 5

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Q: cln 2 0 ex √e²x - 1 dx

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Q: 1. Evaluate each 2-variable function f: D→ R below at the given points. For a point described with a…

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Q: A table of values for f, g, f', and g' is given. g(x) 2 8 2 Xx 1 2 3 f(x) 3 1 7 (a) If h(x) =…

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Q: Find the area of the following region. The region common to the circles r = -8 sin 0 and r=4 The…

A: The region common to circles and

Q: Find the derivative of: -5√x + 3 76 ● Type your answer without fractional or negative exponents. Use…

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Q: Find formulas for dy and Ay if y = x² - 2x + 1. dy =

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Q: The figure shows a telephone wire hanging between two poles at x = -20 and x = 20. The wire hangs in…

A: The figure is shown as,The equation for the wire shape is given as,The length of the wire between…

Q: A particle is moving with the given data. Find the position of the particle. v(t) = 1.5√t, s(4) = 12

A: Given, .Given, s(4)=12.

Q: Find the partial derivatives of the function fz(x, y) fy(x, y) = fry (x, y) = fyz(x, y) = f(x, y) =…

A: Given,

Q: Evaluate the integral by reversing the order of integration. 1 1₁² X 4 y³ + 1 dy dx

A: given

Q: 4. §11.5. Q10. Use appropriate form of the chain rule to find dw/dt. w = √√√1 + x2yz¹x; x = ln t, y…

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Q: Write a polynomial f(x) that satisfies the given conditions. 1 Polynomial of lowest degree with…

A: We are given the two roots of apolynomial and their multiplicities and also the value of the…

Q: A new music company wants to start selling col л(p) 100p-2.5p², where p is the price of a collection…

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Q: 9-x²-y² J 0 e¯(x²+y²+z²)³/² dV.

A: