1. Divide the interval [a,b] into n = 4 subintervals of equal length and compute A) the sum of the areas of approximating rectangles using xi* as midpoints for the function: y=2x-x² [1,2]

Q: Differentiate the function. 4√x + 9x 7x² y' = y =

A: Given that y=4x+9x7x2

Q: Consider the following function: Step 4 of 4: Enter the x-values of any local minima, maxima, and…

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Q: 32. The radius of a circle is increasing at a constant rate of meters per second. What is the rate…

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Q: Suppose that a is the area of a disc with radius r which is expanding in time t measured in seconds.…

A: Given a is the area of a disc with radius r which is expanding in time t measured in seconds.   We…

Q: 3) lim X^ X-O' B) i A) O де D) ∞ a(3) = 3₂ E) nove eriste

A: Given query is to find indicated limit.

Q: 5) Find the divergence of (√x² + + z ²) kî + yî + zk)

A:

Q: a) which of the following is the graph. of y = X² ex # B) 2 of 44 c)

A: Shown below...

Q: Use Right-endpoint Rule with n = 5 to approximate ²x x√x+2dx to 4 decimal places.

A: INTRODUCTION:  The height of the approximating rectangle is calculated using the right endpoint of a…

Q: Topic: Time Rates: Inverse trigonometric functions A balloon leaves the ground 500 feet away from…

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Q: (i) The velocity and acceleration of a particle is given as v= -4i -9j + 5k and a= 6i - j + 3k Find…

A: Given velocity and acceleration vector v = -4i -9j + 5ka = 6i -j + 3k

Q: Find the length of the loop of the given curve. x = 6t - 2t³ y = 6t²

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Q: 11) If the Taylor series of a function has the general expression xn f(x) = En=on! The corresponding…

A: To solve the following problem

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

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Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt

Q: Differentiate the function. F(t) = tº + e⁹ F'(t) =

A: Here is the solution:

Q: Which of the following functions has a horizontal asymptote at y = 7x - 1 8x + 1 Oy= Oy= Oy= 3x² 5 -…

A:

Q: bounded by the following curves: y = x³/2, y = 8, x = 0, y = 0. Find the volume of the solid…

A: Given ,       y = x32 ,  y=8  ,  x= 0 , y=0.  From Shell method-     Since the revolution is around…

Q: 14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

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Q: 3 x³e2x dx

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Q: Find the average value of f on [0, 8]. YA 1 0 2 4 6 X

A: Given :- Find the average value of f on [0,8].

Q: Find the radius of convergence and interval of convergence of the series. n=0 (-2) ¹ 3n+1 -(x + 3)"…

A: NOTE: Refresh your page if you can't see any equations. . the given sequence is  substitute n+1…

Q: 4. Trace the curve: y² = x²−4x−12 x²-2x-3

A: for x intercept put y=0for y intercept put x=0y2=x2-4x-12x2-2x-3

Q: 3. Write 2.734234 = 2.734234234... as an improper fraction.

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Q: The volume of a sphere is increasing at a constant rate of 1827 cubic centimeters per second. At the…

A: To find the rate of change of surface area of sphere.

Q: → R be a function defined by 3x² + x+5 f(x) = not continuous at x = = 0.

A:

Q: (From Briggs) 1. Without evaluating integrals, explain the following equalities. a. b. 7(8-2x) dx =…

A: We need to explain inequalities. As per Bartleby guidelines we can solve one question from multiple…

Q: Find the values of sin(0), cos(0), and tan(0) at the given points on the unit circles in the figure…

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Q: Differentiate. f'(t) = f(t) = 8t t³t-1

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Q: Given the homogeneous differential equation: y (4) + 3y "- 4y=0 What is its auxiliary equation?…

A: Given that the homogeneous differential equation is y(4) + 3y" - 4y = 0 . Here we have to find its…

Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: Find the equation of the line through the y-intercept of y = x²¹ - 9x5 −7+ 9x² and the x-intercept…

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Q: 13. The function has the 1st derivative given by f'(x) = -x(x+3)(x - 1)²(x+4)³. What are the x…

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Q: Find the Equation for the Graph of a Logarithmic Function (-4,3) (2,4)

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Q: A firefly is flying along the path defined by r(t) = 20. At hat point(s) along the firefly's path…

A: Given position vector r( t ) = { t2 , 5-t2 , t3 } r( t ) = t2i + ( 5-t2 )j + t3kas we know that a( t…

Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

A:

Q: 10- You want to invest €1000. What interest rate is required to make this investment grow to €2000…

A:

Q: Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at…

A: find equation of tangent line at ( 2 , 16 ) first find slope  for x = 2  slope m = 8*2 = 16

Q: Use integration by substitution to solve the integral below. Use Cfor the constant of integration.…

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Q: The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 14…

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Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: use derivative and critical points for absolute maxima/absolute minima

Q: X Find the point of inflection of the graph of the function f(x)=2sin on the interval [0, 147]. ○ (7…

A: Given query is to find th point of inflection.

Q: Transform the given differential equation into an equivalent system of first-order differential…

A:

Q: Given the graph below, solve the following inequality: k(t) < 0 +10 +RVEY 9 8 7 6 5 4 3 2 1…

A: To solve the given inequality

Q: X √4- 4+3x² -dx

A:

Q: Use the Divergence Theorem to evaluate the surface integral fF.dS where F(x, y, z) = 2₁ 56.

A: Please see the below picture for detailed solution.

Q: 4 3. After an appropriate trigonometric substitution, the integral ²√²+4 dx becomes (c) / cot (d) S…

A: To evaluate the integral

Q: A tank is full of water. Find the work W required to pump the water out of the spout. Use the fact…

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Q: 2 sin 0, 3. Find a "cartesian" equation for the circle which is given by the polar equation r = and…

A: The polar equation is  r=2 sin θ

Q: Consider the following information. lim f (x) IIC lim g(x) IC (a) (b) (c) 6 Use the information to…

A: To evaluate the given limits of function