1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ 2-3- 1-3 f(x)= { = −x+4 x − 3 x<3 I > 3

Q: Initially 100 milligrams of a radioactive substance was present. After 4 hours the mass had…

A: This question is based on application of diffrential equation.

Q: dx It see ax a) x + 1 (cot ax- csc ax) + c 6) x + 1 ( cot ax + μc ax) + c c) x + £ (cut ax + cac ax)…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

A: The objective is to solve the above question.

Q: Suppose that the piecewise function f is defined by Determine which of the following statements are…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question.Please…

Q: Q4) find the soluation of differention equation using exact equation

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Q: J (tanᎾ - 1)2 dᎾ

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Q: ſº 5u³ – 3u³ – 9du

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Q: dy Find by implicit differentiation. Then find the slope of the graph at the given point. dx 3x³y =…

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Q: Differentiate the function. (2x+5) y= (5x+1) 3 기 dx 11

A: Given:       y=2x+545x+13 differentiating with respect to x Apply the quotient rule:…

Q: x" -2x +x= 15; x (0) = 7, x (0) = -16

A: We have solve the given differentiable equation…

Q: Evaluate the indefinite and definite integral (2e* - 3e-2x) dx

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Q: -9-x²-y² L.**** 1 dz dy dx 0 (a) Sketch each of the following: • the solid E . the projection of E…

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Q: B)Convert 20= tan¹r to cartesian.

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Q: Q:3) A) Test the following surface for maxima minima and saddle point: Z=5+xy+x²+2y+3x

A: See this solution in below

Q: Solve the given differential equation. All solutions should be found. dy 2xy + y² + 6 x² + 2xy dx…

A: First change the given differential equation in the form         M dx + N dy = 0  Then check that…

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Q: The exponential function given y H(t) = 80,031.49(1.0483)', where t is the number of years after…

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

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Q: 3 4 Q4) Suppose a class contains girls, and boys. Suppose that 40% of the girls have long hair, and…

A: Above question is solved.

Q: b. ·(b³ + a³) units³ 3 d. -b³ + a³) units³ 16. The arc length is defined as if y=f(x) is a smooth…

A: We have to find the arc length of the curve y=f(x).   According to guide line we solve only one…

Q: Solve the given initial-value problem. Give the largest interval I over which the solution is…

A: We have to find the solution and the interval.

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: dy = y2-y that passes through the indicated points. dx Find a solution of x (a) (0, 1) y = (b) (0,0)…

A: The solution is given in the next steps.

Q: [ (cosx+2sinx) COSX dx

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Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

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Q: A particle is moving with velocity v(t) = t2-9t + 18 with distance, s measured in meters, left or…

A: The objective is to find instantaneous velocity and speed at time t=5sec.

Q: (1+x)*dx X

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Q: Consider the initial-value problem y' + ey = f(x), y(0) = 1. Express the solution of the IVP for x>0…

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Q: Consider the region R bounded by the curves y = 2 sin(2x) and y = 0 in the interval [0,1] with a…

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Q: (1) (x²+2x) dx = (3 - In x²) dy separable exact linear in x linear in y homogeneous Bernoulli in x…

A: The answers are in step 2

Q: Q2: Find the following limits V-V lim x418√√x+√ 友

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Q: [1 if A= 2 13 23 2 1 -2 find det (A) if 3 3 -1. 6 O 38 O 16 O 18 O 48 O

A: The solution is given in the next step.

Q: Find the solution of each of the following differential equations: a) y'=ye² +2e¹, y(1) = 3 b) 2…

A: I am attaching image so that you understand each and every step.

Q: Find the solution of the given initial value problem. π ty' + 2y = sint, y "(-) = 5, t > 0 Y ||

A: Concept: linear differential equation of the form dydx+Py=Q The general solution of the linear…

Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-2=-2

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Q: Find for THREE of the following functions: dx *²)+In/cos(x)). 5 2(cos(x)))

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Q: Q:5) A) Use the definition to determine whether the series converges or diverges 530+2 اسور

A: First I have written the Ratio test for Convergences of a series and show that , given series is…

Q: 2 ln x + ln (x+1)- 1/2ln (x^2+1). Compress the logarithmic expression.  PRE-CALCULUS HW question..…

A: The given expression,   2 lnx+lnx+1-12lnx2+1

Q: ¹.) f(x) = (x³ - 7x² - 6x + (4 +17) f(x) = x-6 7x - 6 2) f(x) 4 - 17x²

A: Explanation of the answer is as follows

Q: Task 5. What is the domain of the function a) (0, 1) b) (-∞, 1) c) (-∞, 0) U (0, ∞) esin (1/2) y =…

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Q: Show that |7₁7₂|=|z₁||2₂|

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Q: S₁ y² – 3ydy 11

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Q: Find the general solution of the given differential equation, and use to determine how solutions…

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Q: Solve the given differential equation by separation of variables. dp = P - p² dt et+c P = _t+c X

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Q: Determine whether the function is one-to-one. If it is, find a formula for its inverse. f(x) = 9 x+1…

A: Equate fx=fy and determine whether the given function is one to one.        fx=fy…

Q: Find the solution of the given initial value problem in explicit 1 y' = (1 — 11x)y², y(0) = ——— 6…

A: We can solve the given differential equation by using the variable separable method.

Q: 6 + 5 4 3 2 H -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 + The graph above is a transformation…

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Q: If a person's temperature after x hours of strenuous exercise is T(x) = x³ (7- x²) + 98.6 degrees…

A: We have to calculate the rate of change after 1 hours

Q: 2x² + 3 Find f'(x) given that f(x)= x² - 5x+2 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ -…

A: I am attaching image so that you understand each and every step.

Q: Jse a graphing utility to graph the function and estimate the limit. Use a table to reinforce your…

A: Using l hospital rule to get limit