The Distance from P( 5,3) to Q(2,-1) is

Q: 5**+2x (2x3 +1)dx *(2x3+1)dx

A: I have stated the used formulas in the solution.

Q: 25. Evaluate the following definite integrals. c) LIVII – x dx

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Q: the cross section of a trough is a parabolic segment 8 ft wide and 4 ft deep. if the trough is fille...

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Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places acc...

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Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then, ...

A: Given query is to find the average temperature of the coffee in the first 40 min.

Q: Solve for the differential equation

A: Note: In the first question given equation is not clear as only left hand side of the equation is gi...

Q: The instructions for the given integral have two parts, one for the trapezoidal rule and one for Sim...

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Q: Find y' by implicit differentiation 1. x³+y³=6xy 2. x²+y²=4

A: Question 1,Given,           x3+y3=6xyTo find : Find y' by implicit differentiation.

Q: Question 2: Compute the derivative of y = arcsin(cos(arctan(r))).

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Q: Use the price-demand equation below to find E(p), the elasticity of demand. x = f(p) = 12,500 – 325p...

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Q: A hole of radius r is bored through the center of a sphere of radius R. Find the volume V of the rem...

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Q: For each item, graph the function f (x). Use the graph to estimate lim f(x), lim f(x), and lim f(x)....

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Q: I. The Fisher effect theorizes that nominal interest rates observed in financial markets must compen...

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Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. an = 51/n (Use s...

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Q: X-7y=-11 ---(1)  5x+ 2y = -18 ---(2)

A: Note:- As statement of problem is missing for given system of equations so we can solve system of eq...

Q: Find dy by implicit differentiation and evaluate it at the given point. dr tan (9x + 5y) = x, (0,0) ...

A: We know that; The chain rule; fgx'=f'gx·g'x The Power law; ddxxn=nxn-1 And ddxtanx=sec2x   Given: ta...

Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then, ...

A: Solve for average temperature after 40 min. 

Q: Find the derivative of the function. f(x) = 8(x3 - x)4

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Q: 27 The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) ...

A: Given query is to find the height of the ball when it's fall with the rate of 120 ft/sec.

Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y = x2.

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Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: dx 9x2 - 12x-5

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Q: Identify all singular points and points of discontinuity of the given function. (Enter your answers ...

A: The given function is  f(x)=9-xif x≤9x-9if x>9

Q: Integration by trigonometric integrals/substitution: (4-3 cos (x)) sin²(x)dx

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Q: Find the general term of the sequence, starting with n = = 1. Determine whether the sequence converg...

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Q: cos x tan x a) lim x→0 2x (x2 b) lim sin(x-) 4 x- 4

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Q: 3 lim f(r) エーC lim g(r) 12, and lim h(r) = -3. エーHe エー Compute the following limits: a. lim(-4 f(r))...

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Q: 7. Given the space curve er(t) = (4 sin t ,4 cos t , 10t), Find T, N, B, and t (torsion)

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Q: First make a substitution and then use integration by parts to evaluate the integral 9x³e*´ dx Note:...

A: A detailed solution is given below 

Q: The Ideal gas law is given by the equation: pV = nRT where p = pressure, V = volume, n = number of m...

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Q: 10 -X 13 10-x = J3x 10 ニ 3.66 m

A: Topic:-  function   

Q: Solve ( V42 dx then evaluate the answer at x=-39 and C=34

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Q: sinº – cos? –dx 2 2

A: We have to find the integral of the above function.

Q: What trigonometric substitution will you use in solving the below integral? Note: Let W be the angle...

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Q: Find the volume formed by rotating about the y-axis the region enclosed by: 10y and y° = x with y > ...

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Q: Use integration by parts to evaluate the definite integral. 8t² In(t)dt Give an exact answer

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Given: So, here an=1317n-1. Now,                limx→∞ 1317x-1=13·limx→∞ 117x-1=13·limx→∞ 1limx→∞ 1...

Q: dt 4e-t – et

A: I =∫dt4e-t - etI =∫et dt4 - e2 tet = uet dt = duI = ∫ du4 - u2

Q: Find the value of the limit x² + y? lim (x,y)→(0,0) 2x + y (You can consider using the polar substit...

A: Limit  =  0 When both variable are in sum and squared form then trigonometry subsitution results in ...

Q: 5. Find the volume of the solids generated by revolving the regions bounded by the curve to x = 4 ab...

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Q: 3] By using the properties of dot and cross product, prove the following: a) (ü x 7). v = 0. b) (w –...

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Q: S Vx + 3(x + 1)dx

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Q: 2. Write an expression for the nth term of the sequence а) 2, 8, 14, 20 ... 1 1 1 b) 1, 4 ' 9 16

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Q: 19. Differentiate the following functions. g) y = 2 h) y = xsin-1x+ V1- x2

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Q: along the x-axis so that at time t 2 0, the acceleration of the particle is a(t) = 15Vr. ticle is 10...

A: In this question we will use basic concepts of calculus i.e concept of integration. We will use the ...

Q: 16. If f(x) = 2x² + 3x + 5, f(c) = 20, and the interval is [0,5], use the Intermediate Value Theorem...

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Q: Evaluate using substitution techniques

A: Given

Q: Activity x -1 a. Find lim f(x) if f(x)=. x+1 b. Complete the table of values. -2 -1.5 -1.1 -1.001 -1...

A: Limit  and function values 

Q: Find the inverse of the given matrix and verify if [A][A]-1 = [A]=1[A] = [1]: [25 5 [A] = |10 4 8 16...

A: Here, the given matrix is: A=25541051681222 First of all, find the inverse of the matrix.

Q: Sse sech²xtanh²x dx 2.

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