Find the average value of f(x) = over the interval [0, 1]. (3x2 + 3)² Enter the exact answer. fave

Q: 4.(Straightforward) Determine if each of these differential equations is exact, and if so, solve it.…

A: To tell which of them are exact differential equation.

Q: What is the area bounded by:(answer must be fractional form) x²=-9y and y+1=0

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Q: [7 3 -5 Q1\ A- 1- if A = 0 4 and B= 3A;C = B+5I find matrix D such that 1 4 D= 2A+B-C

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Q: sin“ (x)dx 4

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Q: A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south…

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Q: a right circular cone has a base within the radius 15 cm long. its height is 20 cm long. it is then…

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Q: Identify the form of the partial fraction decomposition of the rational function -3x2+10 x²(x+-25)…

A: Given that-3x2+10x2 x4-25Solution:if cxx2-a2…

Q: x'+3x +3x+1 (3) (i) Find lim x+1 2x +3x –1

A: In given function on putting x = -1 it gives ( 0/0) indeterminate form .  Hence first we factorize…

Q: 15. Which of the following has terminating derivative? 1 1. у %3 Зх3 — 2x2 + х-1 —5 II. y Зx+2 1 . у…

A: We will find the terminating derivative.

Q: dy a. Use implicit differentiation to find .xp b. Find the slope of the curve at the given point.…

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Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship…

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Q: 0.8 0.6 0.4 0.2 (c) -0.3 -0.2 -0.1 0.1 0.2 0.3 0.3 0.2 0.1 0.2 0.4 0.8 10 -0.1 -0.2 (d) -0.3 x = 0.5…

A: 1.  x=0.5-0.5ty=1-t2 Answer is (b) 2. x=t3-0.7ty=1-t2answer is graph (c)

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) =…

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Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: The radius of the sphere is increasing at a rate of 5mm/sits diameter is 80 mm

Q: pq21

A: We will find the rate of change of distance between the plane and radar.

Q: The circumference of a sphere was measured to be 72 cm with a possible error of 0.5 cm. Use linear…

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Q: Evaluate the limit, if it exists. (Use symbolic notation and fractions where needed. Enter "DNE" in…

A: Given,            limx→4x-2x-4

Q: Consider the following. u = -6i – 2j – 4k, v = 2j + 2k %3D (a) Find the projection of u onto v. (b)…

A: Given that u=-6i-2j-4kv=2j+2ka.projection of u onto…

Q: The area of the region bounded by the x-axis and y=7x-x2 is revolved about the x-axis. The volume of…

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Q: Find equations of the tangent plane and the normal line to the given surface at the specified point.…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: 1 dx, x > 2 x2 Vx2 – 4

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Q: What is the slope of the tangent to the curve x-y² -x = - 4'at (1,2)

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Q: 12 22, 23 , 2* 5*6*7 *8 * 3. Test the series

A: D' Alembert Ratio Test: Let ∑n=0∞un be a series of positive real numbers such that limn→∞un+1un=L…

Q: y = cosx sinx

A: Given query is to the derivative of the expression.

Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (5,…

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Q: Assume f and g are differentiable functions with h(x) = f(g(x)). Suppose the equation of the line…

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Q: In what way derivative useful to you?

A: Derivatives are used in a variety of subjects, including science, engineering, physics, and others,…

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Determine whether the planes are parallel, orthogonal, or neither. 8x - 7y + z = 7 x + 2y + 6z = 1 O…

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Q: A (4, 270°) (ounter= 909 120° 60° 150° 3.0° 180 0° 210° 330° 240° 300° 270°

A: We have to find the other  three coordinates.

Q: Find the indicated partial derivatives. f(r, s, t) = r In(rs®t®); rss' rst frss(r, s, t) = frse(r,…

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Q: Suppose that f(2) = -5, g(2) = 3, f '(2) = -2, and g'(2) = 4. Find h'(2). (a) h(x) = 4f(x) – 3g(x)…

A: As per our guidelines we are solve only first question you can repost other questions in next…

Q: ind the distance between the point and the plane. (Round your answer to three decimal places.) (5,…

A: We have to find the distance of the plane

Q: Given the following vectors ā = -1,–2),5 = (-3,-4),c = 2,-1),đ = (-4,3) %3D Use the dot product and…

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Q: Find the unit vector of n = (4,-3) .

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Q: aluate the limit assuming that lim,→-4 f(x) = 5 and lim,→-4 g(x) = 2. se symbolic notation and…

A: Topic:- calculus

Q: Find y' and y". y = Vx In(x) y' = y"

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Q: Find the volume of the solid of revolution formed when the area of the region bounded by y3Dx2,…

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Q: The following puzzle was put on the board. We are two natural numbers. Our difference is 30, and our…

A: We have to solve the puzzle

Q: lim .2 X → 00 et?

A: Given query is to find the limit of the expression.

Q: Using two or more complete sentences, describe how you can find a vector parallel to 6 = (-3,2).

A: This question can be solved using the concept of parallel vectors.

Q: Question 3 <0 <t Given Cos(0): 5 and 2 ,what is the value of cos(20)? -21 A 5 B 7 25 16 D 25

A: This question is based on Trigonometric equation.

Q: 4x-6z+5 2+3cosz sin z 9. Find dz.

A: Here we have to integrate the given Integral.

Q: Find the absolute extrema of the function on the closed interval. f(x) = x³ - x?, [-3, 2] minimum…

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Q: mp must make an angi must a 15-foot ramp make with the ground to reach the same window? 30° 16° O…

A: Given query is to find indicated angle.

Q: Question 1 -x2 1 4a?t prove that VE If v = dv ôt

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Q: 2x+1 =(x + 2)5 – 9(x + 2)i + c (x+2)5

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Q: Which of the following could be an example of a function with a range (0 and a domain ) where a> 0…

A: Let's find.

Q: Given vectors ā = (-1,-2),5 = 2,–1), find 4a-35. (10,5) (-10,-5) (-10,5) (10,-5)

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