Find dy if y2T+4+ In(x+2)= xy3 dx y - 2Vx+4 2yvx+4 -3xy 2x+4 2yvx+ 4 y -2 2yvx +4 - 3xy- Vx +4 2yvx + 4 - 3xy

Q: Prove that lim (4x² – 25) = -9. X→2

A: We will prove this by definition of limit as follows 

Q: V -/1+/x - 1 1+/x +1 · IVx tan 2 tan dx 1+/x +1+//1+/x -1 -1

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Q: C. Given: ΔΤΑΝ-ΔΤKJ 1. If TJ = 8cm, AN = 10cm and TA = 12cm. Find TN and KJ 2. TN = 5x -7cm, TJ = x ...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

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Q: x2 3 |5 – x + C а. 5 – x3 - cos t dt 1 + sin t In 1+ sin(t)|+C b.

A: integration

Q: B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)?, and passing throu...

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Q: (a) Find the critical points, if any, of the following function on the given interval. (b) Use a gra...

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Q: Consider the points A(3, -3, 5), B(5, –5, 2), C(-1, –4, 2), and О(4, 1, -8). a) Find the volume of t...

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Q: Evaluate the integral L(9te") i + (9e 2") j+ (4) kļat. J[(otea") i+ (9e 2) j+(4) k]at = ([ i+ +. (Ty...

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Q: iven the ODE, solve: x(x + 4)*dy + [y(x+ 4)* – 3x*y³]dx = 0

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Q: Using the partial fractions technique, the function fx)= 22x+58 can be written as a sum of partial f...

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Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent l...

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Q: The slope of the tangent line to the curve y 2x at the point (- 5, - 250) is: The equation of this t...

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Q: 2x?-8х+7 x 0 x-6x3

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Q: Solve the assigned situation to you and create an appropriate word problem on given values. Show the...

A: It is given that, the foot of the ladder is sliding away at a rate of 1.5 m/s when it is 4 meters fr...

Q: Find the area of the triangle with vertices P(1, 4, –2), Q(0,0,0) and R(4,5, 1). NOTE: Enter the exa...

A: We can find the area as below.

Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

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Q: Ssin (y)cos(y)/3+ sin° (y) + 5e" dy

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Q: Velocity If a stone is thrown down at 100 ft/s from a height of 1,400 feet, its height after t sec...

A: A stone is thrown down at 100 ft/s from a height of 1,400 feet, its height after t seconds is given ...

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

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Q: (a) Find the differential dy of y= /4+ 5x. (b) Evaluate dy for æ = 0, dx = .04. (a) dy dx (b) dy =

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Q: Find the area of the triangle with vertices P(1,3, –4), Q(0,0,0) and R(3, 5, 1). NOTE: Enter the exa...

A: P(1,3,-4)Q(0,0,0)R(3,5,1)

Q: a. Use integrals to show that the circumference of the circle z2 + y? = a² is 27a. %3D b. Find the l...

A: Given that equation of circle x2+y2=a2center of circle 0,0  and radius =aSolution :x2+y2=a2y=±a2-x2o...

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: Fg(x) = 1 Vx-1

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Q: 1.

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Q: 1 Evaluate J (37 + x°) dx

A: On solving this integration we will get

Q: Find the exact value of the expression. cos(160°) cos(25°) + sin(160°) sin(25°)

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Q: CSC r+ sec x Express in terms of sine and cosine. cot x + tanr

A: We know that  cscx=1sinx  , secx=1cosx  , cotx=cosxsinx  and tanx=sinxcosxSubsituting in cscx+secxco...

Q: Your factory is going to manufacture a rectangular container which has a fixed capacity V, with a sq...

A: The Volume of a box with a square base  x by xand height  h is V = x2hh=Vx2The amount of material us...

Q: If a region have axes of symmetry at y = x and y = -x then its centroid is at the origin. True O Fal...

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Q: Write the expression as the sine, cosine, or tangent of an angle. tan(7/15) + tan(4z/5) 1 – tan(x/15...

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Q: 1.Sketch the graph of the following conic: 4x^2-8y^2+24x+4=0 Then determine the focal point and its ...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given Edit 1 by the vectors u, v a...

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Q: Prove that lim (9x* - 25) = -9

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Q: Consider the points A(2, -3, 4), B(4, –5, 1), C'(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of...

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Q: 10 Find the average value of the function ƒ (x) = from x = 7 to x = 9. Write X-5 %3D your answer as ...

A: Given function f(x)=10x-5    ,   x=7 to x=9

Q: 2 -х - 2 - 6x² - 7x, - 3y² – y³\ -y- 2y2

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Q: 5. Which of the has a domain of (-o, +c0)? a. f(x) = x b. f(x) = x2 c. f(x) = x d. f(x) = x*

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Q: Find the area of the parallelogram that has u = 2i – 2j + k and v =j+3k as adjacent sides. %3D NOTE:...

A: We know that, the expression for the area of the parallelogram with adjacent sidesu→ & v→. A=u→×...

Q: 2x2-8х+7 x 0 9x2+5x-3' Suppose f (x) = -4х3 +6х2—15 х-6х3

A:

Q: For items 5-7: Given that f(x)dx = 3 and g(x)dx = 4, evaluate 5. [4 f(x)– 3 g(x)]dx А. 12 В. О С. 24...

A: Let's find. 

Q: 2х2-8х+7 x 0 х-бх3

A: The given function is: f(x)=2x2-8x+79x2+5x-3, x≤0-4x3+6x2-15x-6x3, x>0

Q: (a) Find the critical points, if any, of the following function on the given interval. (b) Determine...

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Q: 1-cost lim sint et-1 + t t t+0

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Q: Given a funchion x-2x if x<く2 2-x if x22 Determine if f s cantinuaus at X:72, f yes, find f(X) and f...

A: To solve this problem we will apply the concept of continuity and differentiability of a function at...

Q: ctoo The improper integral I' dx converges for p<-1. True False

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Q: 5. Simpson's and Trapezium rules 1. A car's speed is recorded at 10 second intervals. The following ...

A: We need to use Simpson's rule to find distance.

Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v ort...

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Q: A particle moves on a straight line with velocity function v(t) = sin ot cos' at. Find the position ...

A: integration