a) lim f(x) X→-3+ (b) _lim_f(x) E 1 0 (c) lim f(x) x--3 (d) lim f(x) x→ 2-

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. = cos(¹x). y…

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Q: Evaluate the following indefinite integral. 8 dt t10 J ← +C

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Q: 8. Show that the function y = ex (sin 2x + cos 2x) is a solution of the equation y" — 2y' + 5y = 0.

A: The given function is; y=ex(sin2x+cos2x) And the given equation is; y''-2y'+5y=0.

Q: d²y If -y = 3x xy then find dy at the dx² point (2, 6) in simplest form. -

A: The function is given by -y = 3x-xy The point is x, y = 2, 6 To evaluate: The value of d2ydx2 at the…

Q: Let Find f (A) (B) el 2 (7) -2x sin x + cos x (C) 1 (D) (E) -√2 (F) 0 (G) 2 (H) None of these

A: Given query is find indicated derivative.

Q: EXERCISES Evaluate each of the following integrals. 43. S Do dz I + ar Q² by using the reciprocal…

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Q: Differentiate the following functions using any method. sin(√1-cos²x) cos³(x) 1. y=

A: Topic = Derivative

Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

A: Given,

Q: Use partial fractions to evaluate the integral. 2x²-1 (4x− 1)(x² +1) S dx

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Q: 0 KIT √1+tan² x dx|

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Q: If tant 7. what is tan (t - π)? Enter the exact answer. tan (t - π) = =

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Q: A chain 10 feet long weighs 8 pounds per foot and is hung from a platform 35 feet above the ground.…

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Q: Find the total area of the shaded region boundeed by the following curves: x = 12y^2 - 12y^3 x =…

A: The given curves are: x=4y2-4y           and            x=12y2-12y3

Q: 10. Refer to the figure and find the volume generated by rotating the given region about the…

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the…

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Q: The world's population grows at the rate of approximately 2 % per year. If it is assumed that the…

A: we need to find the number of years to take the world population double.

Q: Let A = {2,7,8}, B = {-1,2,6,7}, C = {2,4,6,8,10}, D = {{7},{2,4},{6},2 ,8} List each set starting…

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Q: Evaluate the integral by interpreting it in terms of areas. L₁ (5+ √1-x²) dx

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Q: Mrs. Smith switches back and forth between her normal self, Alice, and her intimidate alternate…

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Q: K 111(x)=4x² - 6x +5, solve f(x) = 21. X= (If necessary, round to two decimal places.)

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Q: 5) Evaluate the limit; sin (3x) Tan (3x) a) lim. хэо b) lim X. Sinx X30 1- cos X fin (3001) тилев…

A: We can solve both the questions of question-5 in the below steps by finding the limit.

Q: u = 3i - 5j + 2j and v = 7i + j -2k find the vector projection of u onto v

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Q: Determine the cylinder's absolute max and absolute min given the function f(x, y) = 3x² + 2y² - 4y;…

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Q: Problem 3. We want to estimate (²1/1 X dx. We will use the right sum, left sum, midpoint rule and…

A: Let's calculate L(2),R(2),M(2) and T(2).

Q: IV. Given the functions f(x) = 2x + 5, g(x) = -x² - 6x + 7, and h(x) = the following. Show complete…

A: The objective of the question is evaluate the composition of given functions.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Evaluate the following: 1. lim       √(6-y)  - 2      y-> 2-   y2 - 4 y + 4 2.  lim   |2t-1| -…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: Evaluate each of the following integrals. 15. f (32³+ 8z - 12) dz +72¹ + 12x Ans. 3 In (x + 3) - Inz…

A: To evaluate the integral.

Q: Use linear approximation to approximate √49.4 as follows: Find the equation of the tangent line to…

A:

Q: II. For each of the following ellipses, find the center, principal axis, vertices, co - vertices,…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: = In this problem, we will approximate the value of the definite integral I the Trapezoid Rule. […

A: Concept: One of the significant integration rules is the trapezoidal rule. Because little trapezoids…

Q: Solve each of the following by forming exact differential (2y + 2xy2-xªy)dx +(x³ + 2x2y-x)dy-0

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Q: Suppose a is a positive integer. Simplify the expression a Σ((n + 2)³ + n³ − 2(n+1)³). n=1

A: We need to evaluate∑n=1a((n+2)3+n3-2(n+1)3)

Q: Limits 1. Below is a graph of the function g(x), find each limit as listed below. If the limit does…

A: As per the rules of the company we are supposed to answer the first question and rest can be…

Q: 3. For h(x, y, z) = ln(x² + y² - 1) + y + 6z and the point Po(1, 1,0), find the directions in which…

A: Let's find directional derivative and increases, decreases most rapidly at point Po.

Q: What is the y-intercept of y = sec x?

A: We can find the y-intercept in the below steps.

Q: Find the volume of the solid generated by revolving the region about the y-axis. The region in the…

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Q: On a sketch of y = ln(x), represent the left Riemann sum with n = 2 approximating ſå ln(x) dx. Write…

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Q: Solve the following differential equations. 2y dx + x [ x2ln(y) - 1] dy = 0

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Q: (x, y) = f(x)=x√x + 12 DNE Determine the open intervals on which the graph of the function is…

A: Given query is to find the interval where function is concave up.

Q: A farmer wishes to build a rectangular pen. They have 2,500 dollars to purchase the fencing. The…

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Q: 5. Find the general solution of the DE y" – 4y' — 12y = sin(2t).

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Q: The distance from the point (1, -1, 1) to the point (-3, -3, -3) is 3 AO 5 BO 4 CO 6 DO

A: Solution: Given coordinates are

Q: The cartesian coordinates of the point P is: ← A 0 2 1 32 R P (1, 0, 3) AC (1, 2, 3) BC (1, 2, 0) Co

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Q: Evaluate the indefinite integral: [ (6e" + 5 sec² u) du = = ← + C.

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Q: An open box is to be made from a eighteen-inch by eighteen-inch square piece of material by cutting…

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Q: The population of a city is 140,000. It declines continuously by 4% per year. Assuming this trend…

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Q: Solve 2 sin² (x) + 3 sin(x) + 1 = 0 for all solutions 0 < x < 2π x = Give your answers as a list…

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Q: 1. g(x)=3 tan¹ 3x 2. y=xsin ¹2x+cot ¹ √ 3. f(x) = sin ¹

A: Let's find derivative of given function.

Q: dy Solve the following implicit partial derivative dx and select the correct answer:…

A: sol is given below..