5. Evaluate the following limits: (a) lim Inr xxx (b) lim In r →1-1

Q: Evaluate the following double integral: Jxy da where the region D is the triangular region whose…

A: Here we have given a double integral. ⇒∫∫Dxy dA over the triangular region D with vertices (0, 0),…

Q: Find the following. S (13½√x - 11x³7) dx - 73

A: To calculate the integral. ∫13x4-11x73dx

Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4…

A:

Q: Let L denote the left-endpoint sum using n subintervals. Compute the left sum n 4. for the given…

A: fx=ln1+ex

Q: Find the exact length of the curve. x = et − 9t,    y = 12et⁄2,    0 ≤ t ≤ 5

A: x = et − 9t,    y = 12et⁄2,    0 ≤ t ≤ 5

Q: TT Compute the integral: - -TT sin t 1+ t dt (Hint: sin(t) = sin(t))

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Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

A:

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Evaluate the integral. ror4(1-x²) 1/2 J-₁ Jo x dy dx

A: let  N=∫-10∫04(1-x2)12xdydx

Q: Sketch the region R whose area is given by the iterated integral. 16 *16 - X [²[* y 8 6* [* d 16 14-…

A: To sketch the region R whose area is given by the iterated integral: ∫08∫0x dy dx + ∫816∫016-x dy dx…

Q: 12 The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = 8 The value…

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Q: Determine if the field F = 19y i+ 19(x+z) j-19y k is conservative or not conservative.

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Q: Find a power series for the function, centered at c. f(x) = 00 n=0 1 f(x) = g = x₁ c = 3 Determine…

A: NOTE: Refresh your page if you can't see any equations. . centered at c=3 divide the numerator…

Q: log64x-1=3

A:

Q: 11) Find the sum of the series. 1 n(n + 3) Σ n=1

A: The given series is:  ∑n=1∞ 1n(n+3)

Q: Find and dx dx d²y dx² x = e¹, y = te-t || d²y dx² For which values of t is the curve concave…

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Q: Explain why each of the following integrals is improper. 1. dx X-7 (b) O Since the function y = O…

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Q: 1. Find the surface area of the surfaces described below: (a) The part of the plane 4x +2y+z= 12…

A: (a) To find the surface area of the part of the plane that lies inside the cylinder, we first need…

Q: The direction angles of a nonzero vector a are the angles a, ß, and y (in the interval [0, m]) that…

A: We need to find direction cosine and angles.

Q: the tangent to f(x) = 2x^3+ax+b has a tangent with a gradient 12 at the point (-2,33). find the…

A:

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 57 M8 n=1

A: The given series: ∑n=1∞5nn!We have to use the Ratio Test to determine if the following series…

Q: What are the rectangular coordinates of the point whose spherical coordinates are (5, 7,)? X Y || ||…

A:

Q: 12-11-10-9-8 -6 -5 -4 -3 -3. 6 8 9 10 11 12 Give the period of the function whose graph is shown…

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Q: A 140-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo with radius…

A: Given data for the question is÷

Q: Which of the following functions could make the graph of: A -6 O f(x) = x³ + 2x²+x+2 O f(x)=x²+2x³ +…

A: We have to find the equation of the function f(x)

Q: Consider the following.. (x)=3x²+8x-20 (a) Find the derivative, by using the definition. 7(3) - (b)…

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Q: a) Calculate the exact area bounded by the x-axis and the graph of y=15-8x+x^2…

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

Q: Write the repeating decimal as a fraction. 4.17326326326...

A: We know that the formula 0.326326326......  =326/999

Q: 8 Ν n = 2 (-1)" Δη In(n)

A:

Q: Differentiate each of the following: y = e^Inx

A: given y=elnxformula used→(i) d dx(xn)=nxn-1(ii)  we know→ elna=a

Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

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Q: 7.8 ? 11.2

A: One of the angle of the triangle is 90° hence it is a right angle triangle  As we know that  cosA =…

Q: Determine whether the series converges or

A: Use limit comparison test

Q: an ↓ (-1)"+¹n + √n

A: If the limit n tends to infinity value not equal to zero then the sequence is diverges

Q: Use partial fractions to find the area of the given region. 7 y = -1 16- +² y 3 2 1 J. 1 2 3 4 X

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Q: Find the point on the line 5x+6y−4=0 which is closest to the point (0,−1).

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Q: Use summation properties and formulas to rewrite and evaluate the sum. 25 Σ ((2k)* – k3) k=1

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Q: Given a 23 cos (19t) - 19 and y = 46 sin(19t) + 147 (write the answer in number in the box) (i) (ii)…

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Q: Consider the following vector field. √x 6+z F(x, y, z) = √y j+ 6 +x (a) Find the curl of the vector…

A: function

Q: Find the domain of f(x)= O {x|x€R¸x*−2,2} C O O {x|xeRx=2} {x|x€R¸x÷-4} {x|x€R¸x#4} 4x²-3 (4+x)

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Q: Determine if the following series converges or diverges. Use any method, and give reasons for your…

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Q: Find the volume of the pyramid with base in the plane z = −7 and sides formed by the three planes y…

A: Here we have to use the concept of triple integration

Q: Consider the graph of y = f(x). 3 5 -4 -3 -2 -1 (a) f'(-4)= (b) f'(4) = -1 -2 -3- 2 (c) Determine…

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Q: A particle is moving with the given data. Find the position of the particle, s(t). v(t) = 3 cos(t) +…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

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Q: Identify the field below as conservative or not conservative. F = (9z +9y)i + (5z)j + (5y + 9x)k

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Q: Consider F and C below. F(x, y, z)= yzi + xz j + (xy + 12z) k C is the line segment from (2, 0, -1)…

A: The given vector function: F(x, y, z)=yz i+xz j+(xy+12z) kGiven line segment:  C: from (2, 0, -1) to…

Q: Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none.…

A: Given the function is: g(x)=x3-6x2+4  we have to calculate the relative maxima and minima for this…

Q: a) Integrate by parts, letting dv = √5 - x dx. b) Integrate by substitution. letting y = 5 - X.

A: