What makes a function f(x) continuous at x = c? I. f(c) is defined lim f(x) exists II. X-C III. lim f(x) = f(c) X-C I, II, and III I only II and III only I and II only

Q: Let f denote a piece-wise defined function whose graph on the closed interval [-3,3] is shown below:…

A: we have given the graphf will be decreasing in itervals where its slope is negativewe can observe…

Q: Solve this question yey = 1

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Q: d³y dx3 +69²y dx² - Q.2-Solve the differential equation dy 15 d - 100y = 0 dx

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Q: Question 2 (a) Find the derivative of the function. x3 F(x) = sin(u²) du (b) Find the area of the…

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Q: d- d³y dx3 d²y +6 dx² - Q.2-Solve the differential equation 15 - 100y = 0 dy dx

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Q: d. y""-6y" + 12y' - 8y = 0

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Q: Use the Limit Definition of the Derivative to find f'(x) for the following function. You may NOT use…

A: Using the limit definition of the derivative

Q: d. y'"-6y" + 12y' - 8y = 0

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Q: Assume x and y are functions of a third variable t. If xy = 20 and d = 10, find dy dt dt x = 4.…

A: u.v = uddx v + v

Q: In sketching In (x - 2)² y = ex² determine the intersection of the " curve and the horizontal…

A: Solve the following

Q: Given: f(x, y) = ln[1 + x siny] Find: g² f(x,y) 8x² 2 sin y (1+xsin y)² sin² (1+2 sin y)² 1+2 sin…

A: In this question, we need to find the second partial derivative of the given function.

Q: What is the lim [(ln(2x - 4)) - (ln(x + 3))] 818 ? If your answer is a Whole Number Fraction (+)…

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Q: 3. 21 ) f(x) = 3x + 1 [1,3] n=3 a=1 right left & middle hand rule b=3

A: To find out the left, right and midpoint riemann sum.

Q: 12. DETAILS ZILLDIFFEQMODAP11 1.R.001. Fill in the blank. The symbol C₁ represents a constant. d =…

A: The solution is given below.

Q: √xif x1

A: This question is based on limits and continuity.

Q: What is the lim0+ (=//=²²1)? - If your answer is a Whole Number Fraction (+) Positive Infinity (-)…

A: Let's find limit of the function.

Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

A: The given equation is homogeneous differential equation  (x-y)dx +x dy =0.            On…

Q: Solve the equation 6x^(3)-23x^(2)-6x + 8 = 0 given that x = 4 is a solution. precal

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Q: Solve the differential equation. 6. (w^3 + wz^2 – z) dw + (z^2 + w^2z – w) dz = 0

A: Use exact differential equation concept

Q: Evaluate the line integral F. dr where F(x, y, z) = x²y i+ x³ j+e² tan-¹ z k and C is the curve of…

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Q: f(x) = 5x + 2

A: Given.

Q: Find the partial derivative of z with respect to x z = (3x² + 1) cos(x²y). əz = -2x (3x² + 1)…

A: Given function z=(3x2+1)cos(x2y)

Q: 1. S w²dw √2w-w²

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Q: Aball is launched straight up in the air from a height of 7 feet. Its velocity (feet/second) t…

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Q: Given: ez + xy = 1 Find: əz ?х de dz dz 82 da 8z dz = = -I zez+y -eitz. -*e* ze²+y -ze**-y re**

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Q: Question 1 Consider the function below. f(x) = ex/x (a) Find the intervals on which f is increasing…

A: Explained below

Q: please answer #2 #3 #4 find the transcendental curve sketching and the following a. symmetry b.…

A: Since we are given the multiple number of questions and answered according to the guidelines.

Q: For the function f(x)=x^3-3x+1 defined on the interval -3 ≤x≤3. Find absolute maximum and minimum…

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Q: Find the area between the y-axis and the graph X = 543-2-1 1 2 3 4 5 (y - 3) dy = 6.500 (y - 3) dy =…

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Q: (b) The graph of y-g(x) is shown. Draw the graph of y-g(2x). X

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Q: Question In the figures, are corresponding angles congruent? Are corresponding sides proportional?…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: dy If x³+y³ = 1, what is -? dx² D OC O 22(23 ys 2x(2 − y) y³ 2x y5

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Q: 4. Three collinear vectors, a, b, and c, are such that à = 2²/b b and à = 1/2c. (a) Determine…

A: The objective of the question is determine the knowns.

Q: 5. DETAILS ZILLDIFFEQMODAP11 1.2.011. MY NOTES ASK YOUR TE In this problem, y = C₁e + c₂e is a…

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Q: A large boat is pulled toward a dock by a rope. The rope is attached to the bow of the boat which is…

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Q: The value of a car depreciates exponentially after it is purchased. In other words, V(t) = 20(0.5)t…

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Q: A balloon which maintains the shape of a sphere is being inflated. The rate of change of its volume…

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Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

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Q: Suppose two positive real numbers a and b add to 120. Find the values of a and b that maximize the…

A: Given a+b=120 .....1

Q: Consider the following graph of a function f(x) 7 A. For what value(s) x is f discontinuous? If f is…

A: As per our guidelines, I can answer maximum three sub parts of a question. Since there are multiple…

Q: Find the general solution for the following Second Order Deferential Equation: d²y Q4: dx² - y = ex…

A: The given differential equation is;  d2y/dx2 -y=ex+x2.

Q: 1. Determine the value of each of the following limits if they exist. 1²-21-8 +¹-1 3a) lim- b) lim-…

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Q: Remaining "How Did I Do?" Uses: 2/3 Use the given information to find the unknown value. y varies…

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Q: using the guide below Analyze and sketch the curve (x) = (x-1)² A) Domain, intercepts, asymptotes,…

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Q: Q5: Find the inverse Laplace transform of: f(s) = 3²(²-3)

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Q: How do you evaluate this integral using trigonometric substitution?

A: Here x2 -a2  type we use trigonometry substitution by x=a sec(θ)

Q: Q.1- Evaluate the following integrals (answer two only) a- So √x e-√x dx 1

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Q: wing is Of has a relative minima at x = -3 and x = 3. OIt cannot be determined if has any relative…

A: To find the relative maximum and minimum of the function

Q: 3. A 5-pound monkey is attached to a 20 ft hanging rope that weighs 0.3 lb/ft. the monkey climbs the…

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Q: A particle moves back and forth along a straight line. Its position (in meters), relative to the…

A: Find out the total distance travelled during the first 10 seconds.