If a force of 49 N stretches a spring 0.7 m beyond its natural length, how much work does it take to stretch the spring 5.5 m beyond its natural length? The amount of work done is J. (Simplify your answer.)

Q: The graph of f is given. State the numbers at which f is not differentiable. (Enter your answers as…

A: Note:  1. A function is not differentiable at discontinuity. 2.A function is not differentiable at…

Q: 1. Find y' of tan(x²y) = 3x + y²

A: Given:      tanx2y4=3x+y2 differentiating on both sides   ddxtanx2y4=ddx3x+y2  Applying…

Q: Subtract (4q - 8) from the sum of (3q² – 7q – 4) and (6q² + 6q − 2).

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Q: A curve passes through the point (0, 2) and has the property that the slope of the curve at every…

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Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

A: A detailed solution is given below.

Q: Find the G.S. (6x+y2) dx + (2xy-3y2) dy =o

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Q: A mummy was recently discovered. It now contains 72.7% of its original Carbon 14. About how old is…

A: Given half life of Carbon 14= 5730 years. Given the mummy contains 72.7% of its original Carbon 14.

Q: Q2. Find the area of the triangle (by using vectors) whose vertices are A (0,0,0), B(1,1,1), and…

A: To find the area of the triangle with given vertices.

Q: ← The table shows projections of sales (in billions of dollars) of hepatitis C treatments for a…

A: Given data:-   Year Sales 2012 4.3 2013 4.4 2014 6.5 2015 8.1 2016 9.8

Q: 7- 7+3 7-2 + 3 北

A: Solution ) ( y + 3 )/( y - 2 ) + ( y - 3 )/( y + 1 )  L.C.M. of ( y - 2 ) ( y + 1) = ( y - 2 ) ( y +…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) √er (5 + 6e 6e)7/2 dr

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Q: U Substitution (a) State the Substitution Rule. Explain its connection to the Chain Rul- (b)…

A: Topic = Integration

Q: 3) If x³ ≤ f(x) ≤ x for x in [-1,1], find lim f(x) if it exists. x-0

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Q: when solving for the slope of the secant line how did you solve that ?

A: To be explained : Calculation of slope of Secant line

Q: dz Calculate for z = 4x² + 3y², x = sin(t), y = cos(t) dt

A: Topic- derivative of a function we are given, z=4x2+3y2x=sin(t),y=cos(t)we know…

Q: The base of a solid is the region enclosed by a circle having a radius of 7 cm. Find the volume of…

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Q: Match the equation with its graph. x² + 2z² = 1 X* x.

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Q: The slope of line tangent to y = x² + 2x at P(1,2) is: A. 1 B. 2 C. 3 D. 4

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Q: Differentiate. y=9*• log 3x

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Q: 4. X x - 2 > x; in the form of intervals

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2x 2). 9 = (₁ x ² + ( ₂² ²³

A: we need to eliminate the arbitrary constants.

Q: 2. Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 de)

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Q: Use a grapher to find all local maxima and minima and the values of x where they occur. Give values…

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Q: Given f(x, y, z) = xyz, find fxyy

A: The given function is fx,y,z=xyz We have to find the value of fxyy

Q: Describe the surface. x² + z² = 7 O sphere O ellipsoid O hyperboloid O circular cylinder O elliptic…

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Q: Let f(x)=2x+1, find f(a), f(h +a), the net change, and the average rate of change. I found…

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Q: A. Exact Differential Equations Verify that the following DEs are exact, then find the general…

A: Consider the differential equation               M(x,y) dx +N(x,y) dy =0…

Q: The absolute maximum value is (Use a comma to separate answers at x = as needed.) The absolute…

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Q: Find an equation of the tangent line to the graph of y = B(x) at x = 6 if B(6) = 0 and B'(6) = -1/2

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Q: Find the discontinuities of the function f(x) = = discontinuity and redefine if removable. x-1 ex x…

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Q: Determine the missing coordinates of the points on the graph of the function. (x, y) = (-1 (x, y) =…

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Q: Determine the solution of the 1st Ordered Differential Equa 3(x² + y²)dx + x(x² + 3y² + 6y)dy = when…

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Q: Evaluate the definite integral. [/4 sin(t) dt cos (t)

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Q: Use the step-by-step or Euler method to solve numerically each of the following. (b) dy/dx = x+v,…

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Q: A. g(x) is increasing at x = -7 3. g(x) has a relative minimum at x = -7 C. g(x) is decreasing at x…

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Q: -9y+7z = 5 -11x + 17z = -4 13x + 18y = 4

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Q: 2 1. Find y' of tan(x²y4) = 3x + y²

A: The given differential equation is tan(x2y4)=3x+y2

Q: i) S 3+6x+4x² −2x³ (x4+3x²) ·dx

A: The given integral is (3+6x+4x2-2x3)/(x4+3x2).

Q: .(a) In the 3 Significant Decimal Digits, Rounding system, Floating Point Number System, compute the…

A: Concept: Finding the value of xmid*=a+b2.00error in xmid*=xmid*-xmidrelative error=∆xmidxmid% error…

Q: 7315 Q₁. Find the angle between every two vectors below (Answer two only): a) d=i+2j-k and e--i+j-2k…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 4. A boat is pushed off from a beach at 2m/sec. A man on shore holds a rope, tied to the boat, at a…

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Q: Find the following limits: 1 1 a. lim S+x 5 x-0 x b. x²+1 lim x-1- |x-1| C. -2x lim x++∞ √9x²-3

A: Topic = Limits

Q: Which value of a is NOT in the domain of the function g(x) 7- 42 13x 30 ?

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Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: We have given the dimensions of the cardboard sheet i.e.  Let length is = 13 in.  breadth is = 8 in…

Q: Find z¸and zyif z = x² tan¯¹ (²) — y² tan¯ an-¹) y

A: We need to find zx and zy.

Q: A virus is spreading across an animal shelter. The percentage of animals infected after t days 100…

A: This question can be solved by the concept of functions.

Q: Differentiate y=11x³ +4

A: Given, y=11x3+4

Q: [x²-2 if x≤2] -3x+1 if x>2 Graph the function, f(x)=- x y

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Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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Q: 5 Spending on travel and tourism (in billions of dollars) for the years 1991-2009 is given in the…

A: Concept: Power function: A function having a single term that is the sum of a real number, a…