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Q: Find an equation of the tangent line and normal line to the curve 2 of f(x) f(x). = X -√x + 5x² at…

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Q: Find the volume of the solid enclosed by the surface z = x² + xy² and the planes z = 0, x = 0, x =…

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Q: Find the area of the region bounded to the right by x = 4 - y and to the left by x = y. ܘ →NW+ 2₁…

A: The area under a curve y= f(x) from x=a to x= b is given by

Q: If polynomial 4x^3 -12x^2 + kx + 4 = 0 has root at x=2. Calculate exact values of other two roots

A: As the given equation has a root x=2. Then, we need to put it, to find the value of k. , Now put x=2…

Q: 29 J2 1 √√x-2 dx.

A: Whole solution is given below.

Q: How would you express the equation of a sphere with a center at the origin (0, 0, 0) and a radius of…

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Q: f(x) = ln(x - 2

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Q: ][₁ xyz dS, where S is the cone with parametric equations x = ucos(v), y = usin(v), z = u, 0≤ u≤ 1,0…

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Q: 1 n=n + 8n 13. Show that Σ Ση3. n=1 converges by using the Direct Comparison Test with

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Q: 3. Evaluate fxd4, where D is the region bounded above by the line y = x and below by the circle D x²…

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Q: Write an iterated triple integral in the order dz dy dx for the volume of the tetrahedron cut from…

A: We need to choose correct integral option.

Q: 1. Classify the following as TRUE or FALSE. a. All integers are rational. b. If a number is…

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Q: For the following parts, do not round your answer at any point. For any N>0, suppose that there is a…

A: It is given to us that,  Taking square root on both sides,Taking reciprocal on LHS which reverses…

Q: Subject: calculus  Solve the system of nonlinear equations ((2x)^2/3) +( y ^2/3)= (9^1/3)…

A: x=     , y=x=,  y=x=, y=x=,   y=

Q: To produce x units of a religious medal costs C(x)= 12x+63. The revenue is R(x) = 33x. Both cost and…

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Q: Find the critical point of the function f(x, y) = 6 -3x+4x² - 5y - 4y² 7800 5000 8 This critical…

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Q: Find the slope(s) of the tangent line(s) to f(x)=x³ that contains the point (2,0)

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Q: Find h(x, y) = g(f(x, y)). h(x, y) = g(t) = t + In(t), f(x, y) = 4-xy 5+x²y² +In 4 - xy 5 + x²y² X…

A: Given: To Find: To find .To find the set of points at which  is continuous.

Q: all values of x for which the matrix x² - 1 -3 2 20² +4 4xc -1 e. Determine x x+1 -3

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Q: A region bounded by f(x) = x, y = 0, x = 1, and x = 4 is shown below. Find the volume of the solid…

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Q: Write an iterated integral for R described to the right using a. vertical cross-sections, b.…

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Q: Question 8 Match each system of equation to the description of its solutions. 3x-9y+ 6z = 15 2x-6y +…

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Q: the second image is not loading?

A: Here we will use the ratio test for convergence of series

Q: Given the function f(x,y) = 4y-6x, answer the following questions. a. Find the function's domain. b.…

A: Given,f(x, y) = 4y - 6x(d)We have to tell the boundary of the function domain

Q: A package to be mailed using a certain postal service may not measure more than 114 inches in length…

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Q: For each of the following functions, find the maximum and minimum values of the function on the…

A: Solving the problem

Q: (a) Find (b) Hence evaluate d -1 dx (2x2+1)³ 1 So 12x (2x² + 1)4 d.x.

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Q: b. SET-UP only the definite integral using cylindrical shell method that will give the volume of the…

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Q: Find the dimensions of the rectangle of the largest area that can be inscribed in an isosceles…

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Q: In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000+…

A: Given that,

Q: 2) Find the value of a and b such that the function f is differentiable everywhere. f(x) = Jar³, x²…

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Q: n n=21n3 + 1 +1 39. Σ

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Q: Evaluate O A. OB. O C. O D. -2 (2) (1) -² (+-) 2 - dt at t = for the function w(x,y,z)=- 4 9 xy ()…

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Q: Use a graph or level curves or both to find the local maximum and minimum values and saddle point(s)…

A: Function :f(x,y) = 3(x – y)e–x² – y²Find Local Maximum, Local Minimum and Saddle Point.

Q: D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the…

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Q: Find the directional derivative of f(x, y, z) = x² + y² at the point (3, 1, 2) in the direction of a…

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Q: 10. A light is mounted on top of a 16 ft tall pole. A man 5 ft and 6 in tall is walking away from…

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Q: Evaluate O A. O B. O O D. dw dt -2² (²) 2(127) I -2 at t= 2(727) 4 9 -1/² 3 N|W for the function…

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Q: ¬ f(x, y) = −1+7x − 6x² - 7y+5y² -

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Q: The current I(t) in an LC series circuit is governed by the initial value problem below. Determine…

A: The given initial value problem is:

Q: (9) Find the derivative: f(x) = cos(lnx) + log₁0 x

A: 9.The function is

Q: If y = (sin x)², then find O O dy dx (sin x)ª (x cot ä + ln(sin x)) (sin x)” (x cos x + sin x) (sin…

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Q: You will integrate the following rational function: 20x+5 da S (x-7)(x²-4x+8) To do this, start by…

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Q: 47. y = -2 48. y = 8 In Exercises 49-56, use the most convenient method (Disk or She Method) to find…

A: By using the most convenient method (Disk or Shell Method) to find the the given volume of…

Q: Find the equation of the tangent to the curve y = (x − 2)√√√x² +9

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Q: (e) If n(x) = eg(x)+x lim xf(x) x-4 find n' (2)=

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Q: Find the limit. lim (x,y) → - (49-49) 2 2 x+y#49 x+y-49 √x+y-7

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Q: Find the limit. lim (x,y) →(18,18) x+y #36 O A. 6 O B. 12 x + y - 36 x+y - 6 OC. 0 OD. There is no…

A: We need to find the value of the given limit.

Q: Eric spent a total of $50.75 at the school bookstore. He bought a calculator for $29.75 and some…

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Q: Evaluate the double integral over the given region. SS R 1 (x + 1)(y + 1) A. In 7 In 8 B. 8 In 7 O…

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