3. Sketch OP = (3, -4, -2) including the rectangular prism that frames it. Use and label the axes, including the scale, and point P. It is not necessary to label the other vertices.

Q: 7. Let f(x, y) = In(x)+2 ln(y) – x – 4y. Find the critical point of f and determine if it is a local...

A: Let's find. 

Q: If lim,→2 f(x) = 4 and lim, +2 g(x) = 7.Use %3D these facts and limit laws to evaluate lim, 2[3f(x) ...

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Q: 52-56 Find the limits as x → ∞ and as x → 0o. Use this infor- mation, together with intercepts, to g...

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Q: Evaluate the following limits. a. lim?→3 √x^2 −5−2  b. lim?→64 3√x−4  / √x−8

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A: Given that: Graph of an ellipse.

Q: (х+2)* x² – 4 dy 2y dx x? - 4 х —

A: Given  :        dydx+2yx2-4 = x+22x2-4

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Q: Find the derivative of the function. y = 9Vx y' = %3D

A: Our Aim is to find the derivative of y=9x -(i)

Q: If $2,000 is invested at 7% compounded monthly, what is the balance after 8 years? $3,601.84 $3,490....

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Q: Use the cylindrical shell method to find the volume of the solid obtained by rotating the region bou...

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Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818.=

A: Let X equal the decimal number. X=0.904818181818...             (1) With 2 digits in the repeating d...

Q: – ydx + (x + Vxy )dy = 0

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Q: Calculate the vector field flow g⟶ (x,y,z) = (y) î - (x) j + (x + y) k, counterclockwise, along the ...

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Q: Salve for x if Arc tan (1- x) + Arc tan (1 + x) = Arc tan

A: Our Aim is to solve for 'x' if tan-11-x+tan-11+x=tan-1x -(i)

Q: 6. Let f(x, y) = x3 – xy+ y. Find the critical points off and determine if they are local minima, lo...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: 3. f (x) = V1+ v1 – x 4. у %3

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Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

A: The given function y=71-14x2

Q: Exercises 19–22, show there is a number c, with 0 ≤ c ≤ 1, such that f(c) = 0.  19. F(x) = x3 +x2- 1

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Q: An environmental study in a community shows that the level of a certain pollutant in the air is L(P)...

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Q: limit

A: Please refer to the image below

Q: E valuate sin" e cae de

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Q: (n + 2) - n sequence converges to a+2) -星 sequence does not converge.

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Q: Express the repeating decimal as a fraction. 0.2513 23 23 23...

A: topic - rational numbers

Q: Differentiate the following function. Use any method and show the step-bystep solution. b. m = (2...

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Q: Which of the following is the formula for finding the distance between two points on the coordinate ...

A: The formula for finding distance between two points (x1,y1) and (x2,y2) is, d=(x2-x1)2+(y2-y1)2 Opti...

Q: Given the function g(x) = 8x° – 60x + 96x, find the first derivative, g'(x). g'(x) = Notice that g'(...

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Q: A tank contains 60 kg of salt and 1000 L of water. A solution of concentration .03 kg of salt per l...

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Q: Find the angle between A = 10a + 2a and B = - 4a + 0. 5a¸ , using dot product. Answer:

A: As we know that, The expression for the angle between the two vectors is: θ=cos-1A→·B→A→B→ Given: A→...

Q: Determine the value(s) of x for which the following function is discontinuous. Identify the type of ...

A: The given function,         fx=2x2+3x-2x+2 Removable discontinuous:    If a function f(x) has remova...

Q: Find the slope of the tangent lines on the curve y = 6x^3 +24x^2 -39x -43 at poins (-5, 2) and (1/3,...

A: We know that, The slope of the tangent line to the curve at a given point Px1,y1 is equal to the der...

Q: Evaluate the following indefinite integral. Use C for constant of integration. * cos(10x) + sin(20x)...

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Q: f(x)={x^2-8x+16, if x 3 find a and b such that the function f(x) is differentiable everywhere. (HI...

A: Given the query is to find the value of a and b.

Q: The cost to transport a mobile home depends on the distance, x, in miles that the home is moved. Let...

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Q: Q1. A Find by using chain rule, if f= u + cos'u u = x, at x=; marks) B) Graph the trigonometric func...

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Q: Evaluate the integral. 8 r log 4(x + 8) x +8 xp-

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Q: dy 3. 9-49y²

A: To find out the integration. 

Q: 8. The rate at which ice is melting in a small fish pond is given by dv %3D dt V1 + 2, where V is th...

A: Let's find. 

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,...

Q: Now recall the general version of the power rule, where n is any real number. d = nx" – 1 dx Applyin...

A: Basic derivative problem

Q: Written Works Find the equation of the tangent line to the following functions at the specified poin...

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Q: To evaluate: The integral function x2 +x + 1 -dx. (x² + 1)²

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Q: Write the equation of the parabola in standard form sati 1. Vertex (1, – 9); Focus (- 3, - 9)

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Q: Let f(x) = 3 6e". Enter an antiderivative of f(x)

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Q: The base of a solid is the region in the first quadrant bounded by the curves below. 25y = 25 – x2 x...

A: Given : Base of a solid bounded by the curves 25y=25-x2 , x-axis ,and y-axis. In the first quadrant ...

Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: The distance of a particle from some fixed point is given by the following function. s(t) =t +4t-3 a...

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Q: Use the Reimann ntegral to evaluateS vdv.

A: In this question we have to find the Reimann Integral.

Q: 4. If ā= 3i - 2j and b=-5i- j, express 3 a -b in terms of i and j.

A: This is a vector problem

Q: Find lim,-1 f(x) -3 -2 -1 2 O lim,→-1 f(x) = 2 O lim,-1 f(x) = 1 O lim,-1f(x) = -1 Lx→-1 f(x) = –1 O...

A: