Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular to the line = y

Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² + x)))

A: The given limit is limx→0-xlnsin4x2+x. We have to solve the limit using L'Hpotial's rule.

Q: (x + 1) dy = −y + 20 dx O separable exact linear in x linear in y O homogeneous Bernoulli in x…

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Q: Using the concept of the derivative of sin x, what is the antiderivative of sin x? -2 cos x + C 2…

A: We know that: ddx(cos x)=-sin x...(1)

Q: What is the equation of the tangent line to the curve y = x^ + 2x? −x+8 +2x2 where x = 1? y = 7x - 3…

A: Let's find equation of tangent line.

Q: olve the differential equation y"+4y=sec(2t).

A: To solve the following differential equation  y''+4y=sec(2t).

Q: The area in the first quadrant under the curve y = e-x is revolved about the x-axis.  Find the…

A: Topic = Volume

Q: Which function is Chain Rule most useful for? Composite function Polynomial function Logarithmic…

A: In Differentiation chain rule is important tool for differentiating composite function .

Q: Consider the f (x, y) = By evaluating Show 4 at and Hence function 3 y³ + 3x²y - 6x ² the 2 6x² -…

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Q: 7. Find the volume of the solid generated by revolving about the x-axis the region in the first…

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Q: find the higher partial derivative of the following

A: Solve the following

Q: Give an equation of the vertical asymptote of O y = 2 ○ y = 0 O There is no vertical ymptote. Ox=0 y…

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Q: Question 2 Evaluate: Express your answer in three decimal places. limx→8 e-2 a-8

A: The objective is to evaluate the limit.

Q: € G x² y" + (y²)² = ں

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Q: Evaluate the following integrals. y = f(x) a. b. C. d. 16 0 f(x) dx [f(x) dx Ja (2|f(x) +3f(x) dx…

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Q: Evaluate: Express your answer in three decimal places. 3x-2 limx→8 2-8

A: limx→ 8x3-2x-8       00 formApply L'Hopital's rule,=limx→ 813x231Plug in the value x=8=13·…

Q: (1) IF: ā=21-j+ k, b=i+2j- 3k, č=-3i+2j+ k Find : a.b, ã.č, č.ã‚ (a+b).(a−b),(ã+ê).(ā-č) (a +2b-3c).…

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Q: 1) lim (tan x) cos x X-2

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: C. 6x³ +11x² - 4x -3/5 18x² +22x-4dx

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Q: The equation, with a restriction on x, is the terminal side of an angle 0 in standard position.…

A: Solution: 2x+y=0, x≥0 y = -2x

Q: Given w = xe¯ª + ln(x²yz³). Determine δω ?х ?w dx 2 = -xe tết xyz³ dw = xe¯* + 1 + 1²/12 8x dw…

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Q: Find the area of the region bounded above by y = sin(x) and below by y = cos(x 2 1.5 4 0.5+ X

A: Using horizontal /vertical strip

Q: 10 5(5+10) a/n A ナ B 5+10

A: See the details solution in below

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: Find the area of the triangle in IR³ that has vertices P₁= (1, 0, 1), P₂=(2, 3, 1) and Ps= (0, 2,…

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Q: What is the limx→5 5x + 2? 3 5 1 27 1 3

A: To evaluate: limx→5 5x+23 Let y = limx→5 5x+23 y = limx→5 5x+213

Q: What is the equation of the curve that passes through the point (-2,3) and whose slope function is…

A: In this question, we need to find the equation of curve from the given options.

Q: Use first principles definition of the derivative to find f'(x) for the function 3 f(x)= x-2 =

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Q: A full tank consists of a hemisphere of radius 4 m surmounted by a circular cylinder of the same…

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Q: A small hole on the sack of rice cause some rice to be wasted while the sack is being lifted…

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Q: Find f'(a) using the definition of the derivative at a point for f(x) = 1 VI at a = 7.

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Q: A manufacturer has determined that the weekly profit from the sale of x items is given by the…

A: SOLUTION-

Q: What is the limo+ sin(y) In(y)? For answers write... that are in decimal form and round off to…

A:

Q: Question 3 Sketch the following function fully: €²-2²-1 y= ²-4 Upload Choose a File

A: Given function, y= (ex-x2-1)/(x2-4)

Q: For the function y = (x − 2) In x, what are the two x intercepts, and between the two intercepts, is…

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Q: Find the area between the y-axis and the graph X = 543-2-1 1 2 3 4 5 (y - 3) dy = 6.500 (y - 3) dy =…

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Q: A ball is thrown eastward into the air from the origin. The initial velocity is (50, 0, 80), with…

A: Solution  As per given data, Initial velocity 'v'=(50,0,80) Acceleration vector 'u'=(0,-4,-32) As…

Q: x + 2 lim x2x²-4

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Q: 8. 1 (1+x)√√x / dx

A: We have to find out integral

Q: Aball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t…

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Q: What is the slope of the tangent line to the curve y = at the point (3,)?

A: What is the slope of the tangent line to the curve y=1x at a point 3, 13 ?

Q: Express the number as a ratio of integers. 3.898 3.898898898...

A: 3.898898898..... this can be written as  3.898898898..=3+ 0.898 + 0.000898 + 0.000000898 + .. ...  .…

Q: Find a general formula for f(n) f(x) = (x-2)-¹ (Use symbolic notation and fractions where needed.)…

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Q: Jo xy ds where C is the line segment from (2,0) to (5, 4). Evaluate the line integral

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Q: What is the derivative of y = √x? 1 1 X 2 2 1 √x X 2 1 2 X 22

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Q: Find the area under the graph y = x 3 on the interval [1, 8]. 1 2 3 4 5 6 7 8 9 -NW 01 5- 4 3 2 क्त…

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Q: Use the Integral Test to determine whether the series is convergent or divergent. nhe-n n = 1…

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Q: A balloon which maintains the shape of a sphere is being inflated. The rate of change of its volume…

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Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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Q: The number of bacteria in a refrigerated food product is given by N(T) = 23T² – 96T + 12, 5 < T < 35…

A: The number of bacteria in a refrigerated food product is given by N(T) = 23T2-96T+12,  5&lt;T&lt;35…

Q: Identify ALL the Indeterminate forms involved and determine the limit of: limo+ (cos(x))"

A: See the answer below