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Q: Use integration to find a general solution of the differential equation. (Use C for the constant of ...

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Q: In Exercises 47-60, solve the initial value problem.

A: We have to solve given intial value problem. dydt=3-2t,  y0=-5

Q: Determine the intervals upon which the given function is increasing or decreasing. f(x) = 3x - 12x I...

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Q: P @Preve that a)fog is ene to ene Brove thal O (fogl' 6)=Glof)() ouf: Let f amd a be one-to-ene func...

A: Let f:A→B and g:C→A be one-to-one function. (a) To prove: f∘g:C→B is one-to-one Let x and y be any t...

Q: I will appreciate a detailed answer, so I can do by meself on a similar question.

A: Given interval is x=1 to 3 find out deltax using the interval △x=b-ana=1, b=3, n=8△x=3-18=14 Width i...

Q: find (g o f)(x)

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Q: Computing torque Answer the following questions about torque.

A: Given that r=OP=i+j+kF=20,0,0=20i+0j+0k  

Q: Verify that the general solution satisfies the differential equation. Then find the particular solut...

A: To verify the general solution satisfying the differential equation:                                ...

Q: A circle is inside a square.The radius of the circle is decreasing at a rate of 5 meters per hour an...

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Q: Find ay 3.y= log (x-)3 m Cxt2)^]

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Q: The general solution of V – 2x)dx+(2xy+ 1)dy=0 is?

A: (y2-2x)dx+(2xy+1)dy=0y2dx-2xdx+2xydy+dy=0y2dx+2xydy-2xdx+dy=0d(xy2)-2xdx+dy=0Now integrate both side...

Q: How do I find the derivative.

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Q: Find the absolute extrema of the function f(x)= (x+2)4 (x2 -8)2  on the interval [-4,1].

A: Given,f(x)=x+22x2-82 An absolute extremum of a function in a given interval is the point at which a ...

Q: Please show step by step instructions

A: a) the points at which the tangent is parallel to the x-axis are the points at which the derivative ...

Q: In Exercises 41-44, verify by differentiation.

A: Evaluate, ∫x+136dx        ...(1)

Q: Suppose f(T/3) = 4 and f '(T/3) = -3, and let g(x) = f(x) sin(x) and h(x) = cos(x)/f(x). Find the fo...

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Q: anser n Los Angel each, and plastic books sell for $15 each. Suppose that each hardcover book costs ...

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Q: Two sides of a triangle are 9 m and 10 m in length and the angle between them is increasing at a rat...

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Q: Find the focus, the directrix, and the vertex of the parabolax^2 − x + 3y − 2 = 0

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Q: 17

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Q: Let f(x, y) = 3x 2 − 5x 3y 2 + y 4 . Calculate all 1st and 2nd order partial derivatives of f.

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Q: 1 Determine the maximum value of the function fz) = 2x -x - 4 at the interval x e [-1,1]. A -4 в о C...

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Q: 5-

A: Note:- Answer is given in the picture

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the oute...

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Q: 11. A balloon rises at a rate of 4 meters per second from a point on the ground 40 meters from an ob...

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Q: Let f(x, y) = x 2 − y. Sketch the level curves for f = −2, 0, 1.

A: Given fx,y=x2-y

Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t.(a) If dx/dt = 9, find dy/dt when...

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt    ∵dxdx=12x=122x+1·2dxdt+0=12x...

Q: Sketch the graph of a function that meets the following conditions: a. Graphed on the interval [-4,1...

A: Given: a. Graphed on the interval [-4,10]. b. Has no relative extrema. c. Has an absolute maximum at...

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded b...

A: We first sketch the region using a graphing calculator  

Q: Determine whether the integral is convergent or divergent. 1 dx a (x - 7)32 O convergent O divergent...

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Q: Find the open intervals on which the function f(x)=x+6sqrt 1-x is increasing or decreasing. If the f...

A: Consider the given function fx=x+61-x The domain of the given function  1-x≥0x≤1

Q: Please show step by step instructions for each part. For the function below, determine each of the f...

A: (a) Consider the provided function gx=4x8+32x7-14. Find the critical point of the provided function....

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Q: The Power Rule for Rational Functions. Assume that p and q are non-zero integers.Then   d/dx(xp/q) =...

A: We know  ddx(xn)=nxn-1 Here n=p/q  

Q: find the general form of an equatoin for the perpendicular bisector of the segment AB where A=(-1,2)...

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Q: Two concentric circles are expanding, the outer radius at the rate of 5 ft/sec and the inner one at ...

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Q: On a recent trip to the convenience store, you picked up 1 gallon of milk, 7 bottles of water, and 4...

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Q: 18h

A: Given: r→(t)=<sin t, t, cos t> We have to find V→(0): To get V→(t) : Differentiate r→(t) with ...

Q: Find the deviratuce of the functuons: fle) = h v s Hheve a shortest way? please eeplam

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Q: write in standard(vertex) form the equation for the parabola which has the following properties: zer...

A: Given, Parabola equation has zeros at x=1 and x=7. Maximum value = 12 The standard form of the equat...

Q: Verify the identity. (cot x + tan x)4 = csc* x sec4 x Use the Reciprocal and Pythagorean Identities ...

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Q: 2. Use polar coordinates to find the limit. [ Please note that if (r,0)are polar coordinates of the ...

A: Consider the limit  limx,y→0,0e−x2+y2−1x2+y2    

Q: Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 12z) k C is the line segment from (2, 0, -1...

A: Given, part (a): Fx,y,z=yzi+xzj+(xy+12z)k C is the line segment from (2,0,-1) to (4,6,1) We have to ...

Q: Prove that the centroid of any triangle is located at the point of intersection of the medians. Hint...

A: Consider the equation  

Q: Evaluate the line integral, where C is the given curve. xevZ ds, C is the line segment from (0, 0, 0...

A: Consider the  line integral ∫Cxeyzds Where C is the line segment from (0,0,0) to (3,4,2).  

Q: find (f o g)(x)

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Q: 15-

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.