B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)² , and passing through the point (2,1) .

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

A:

Q: 2. f (x) 3 - 2x² if xくQ こ 2 メ if x 2 2

A: f(x)= x3-2x2 ; x<22-x ; x≥2       a=2 , if f is differentiable , then f'(2) should be finiteusing...

Q: Activity 3! Ve the following problems. 1. A city is of a circular shape. The area of the city is gro...

A: 1.Area of circular city;A=π r2differentiating w.r.t. r;dAdt=2πr drdtdAdt=2  mi2yearat r=15 mi2=2π(15...

Q: Let y = 5x² + 5x + 3. Find the differential dy when x = 1 and dx = 0.1 %D %3D Find the differential ...

A: Topic = Derivative

Q: 1 Evaluate the following integral. dx X4V9-x2

A: ∫vn dv = vn+1n+1+C

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Q: Find the fifth partial sum, S5 =E=14( n-1 4(2"*. Write as a fraction reduced to lowest terms in the ...

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Q: Since the start of July, OHaganBooks.com has seen its weekly sales increase. OHaganBooks.com fits th...

A: Let's find. 

Q: S3(*-4y")(>'+14y*-7)' dy

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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: S(6w +12w) Vw + w° dw

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Q: Discuss the continuity of the function h(x) = }" (x2 + 7х -5, x3 – 2x2 + 1, x < 3 x 2 3 on the inter...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: Use the position function s(t) = -16t2 + vt + s, for free-falling objects. %3D A ball is thrown stra...

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Ki...

Q: Consider a closed rectangular box with a square base with side length `x` and height 'y'. Find the s...

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Q: х+3if x1 6. lim x→1 f(x) f(x)

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Q: 1. Calculate the area enclosed by the line y 2x + 3, the x-axis, and the lines x 1 and x- 3.

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: a)a→=-3 i + 8 jUnit vector as the same direction;u= a→a→ =(-3 i + 8 j)(-3)2+(8)2u=(-3 i + 8 j)73u=-3...

Q: Activity 2: Express y in terms of x in the given equations if it is possible. 1. 2x+y=8

A:

Q: Let a = ci +jand b = 3i + 4j. Find c so that the angle between a and b is- 9. %3D Round your answers...

A:

Q: . lim,0+ (1 + 2x)In(2z)

A: Solution :1∞  formif limx→0fx=1 limx→0gx=∞if the form limx→0 fxgx then elimx→0 fx-1gx

Q: Consider the points A(3, – 1, 3), B(4, –3,0), C(-2, –2,0), and D(6, 3, –5). (a) Find the volume of t...

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Q: Let a = ci + jand b = 20i + 21j. Find c so that the angle between a and bis Round your answers to fo...

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Q: Write an equivalent first-order differential equation and initial condition for y. y= -1+ ](5t - 3y(...

A:

Q: Select ALL possible answers if there is more than one. Below shows the graphs of the slopes of the t...

A: The slope of the tangent line represent the derivative of the function.

Q: If 5æ? + 3x + xy = 1 and y(1) = -7, find y'(1) by implicit differentiation. y(1) =

A:

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: Find the derivative of g(x) =

A:

Q: e area between the two loops of the limacon r = 1+2 sin 0.

A: We are asked to find the area between the loops.

Q: 1. Use the e - d definition of the limit to show the following: (a) lim(5x – 2) = 3 エ→1 (b) lim Vr =...

A: The objective is to use definition of limit to prove the above question.

Q: Evaluate the integrals that converge 32 1 dx 2 ㅇ x5

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: 5x + 2 lim log + 6 10x + 12 ° X-

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Q: Jun has decided to save money roughly P25 per week. Suppose he makes weekly deposits of this money i...

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Q: Activity 4: 1. Find the indicated derivative for each of the following functions and evaluate as ind...

A: We know, ddxxn=nx(n-1) , for any real number n. ddxcos x= -sin x ddxsin x= cos x

Q: Below shows the graphs of the slopes of the tangent line of four different functions. Which of the f...

A: A) First graph is the type of =   - x2n And we know that these types of graph attains every value of...

Q: dy – 4y = x*e* 12. x- dx

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Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact answe...

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Q: If $P is invested for n years at 12% compounded continuously, the future value that results after n ...

A: We will find the rate of change of the future value. 

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→ &amp; v→. A=u→×...

Q: (2x2- 8х + 7 | 9x2 + 5x – 3' -4x3+6x2 – 15 Suppose f (x) x > 0 x – 6x3 Evaluate as lim f(x) X00

A: Let's find. 

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

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

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Q: Prove that lim(4x2 – 25) = -9 x-2

A: First we use the formula a2-b2=(a-b)(a+b) then put the limit.

Q: Find the equation of the tangent line at the given point 1 ·y =- X - 3 ; (0, -३) 3*

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Q: Solve the problem in simplest form and complete solution. Find u and du if possible. coss 2x dx | si...

A: Given: I=∫cos52xsin22xdx  ...1   We know that; The Power rule: ∫xndx=∫xn+1n+1+C ; n≠-1  

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: 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: y = e2x, y = e*, and x = 2

A:

Q: Let f(x) = 2x2 – 8x + 14 The slope of the tangent line to the graph of f(x) at the point (2, 6) is T...

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the ...

Q: If 69 + 5 f(x) + 2x²(f(x))³ = 0 and f(1) = -3, find f'(1). f'(1) =

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