In Exercises 7–8, is the function continuous on the interval?

Q: Explain how the first derivative of a function determines where the function is increasing and decre...

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Q: A particle moves along the x-axis from x = 8 to x = 29. Find the work done by the force F(x) 4x2 - 6...

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Q: Sketch the graphs of the following function. f (x) = 4/3x3 - 2x2 + x

A: Sketch the graph of the following function. f (x) = 4/3x3 - 2x2 + x

Q: O fend the values ofxlat which the fallocwing funchrons afe daanhin unus Pcx-ペースXー+3 fcx)= none none...

A: We have to find the point of discontinuity.

Q: -1 -3 Let A = and B = -3 3 Find each matrix below. If a matrix is not defined, click on "Undefined"....

A: A is matrix of order 2×2 and B is also matrix  of order 2×2  Hence AB and BA both are defined

Q: Evaluate the indefinite integral  (integral) x ln(x2) dx

A: Explanation of the solution is given below...

Q: let A = si-j+ k which pairs of vectors ave @ perpendicular. ? O parallel. ? B=i-SK, f C=-15i+3j-3K. ...

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Q: For each of the following problems differentiate the given function. 1. T(=)=2 cos()-6cos ()

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Q: Solve the inequality x3 - 5x2 / x2 - 4 all greater than or equal to zero

A: To find the solution we use inequality method .

Q: 13. Prove: If a function f is differentiable at some a in its domain, then f is also continuous at a...

A: We have a property that, "Every differentiable function is continuous but every continuous function ...

Q: Please answer it the same way provided

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Q: 3 Let A = and D = 6. 6 -7 Find A+D.

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Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant mult...

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Q: Please answer it the same way provided

A: We have to prove

Q: Second order differential equation

A: We have to find the solution

Q: 2. Find the slope of the curve at the point indicated. y = 5x – 3x2,x = 1 a. X-1 b. y = ,x = 0 x+1

A: (a)y=5x-3x2, x=1slope=dydx=ddx(5x-3x2)=5-6xat  x=1slope=5-6(1)          =-1   Ans

Q: Find the maximum area of a rectangle inscribed in a semicircle  of radius 5 inches if its base lies ...

A: Consider the given information as The maximum area of a rectangle inscribed in a semicircle  of radi...

Q: Q6 The area of the region in the first quadrent that is bounded by f(x) sin(2x) , and g(x) = cosx eq...

A: We need to evaluate the area of the region in the first quadrant that is bounded by the following fu...

Q: Q2/ Graph the function bellow, write its Range and Domain, test if it I or is Odd or Even, and its s...

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Q: Please answer with full work

A: Given: fx=3x3x-1for -10≤x≤10 To Find: Maximum and Minimum Value Concept: First Derivative Test for E...

Q: Prove using Delta - epsilon  7. Iimx-> 4 (15-8x)= -17

A: By using definition of limit 

Q: Q3/ Evaluate the followings: 3) L, 4-* In 2 dx

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Q: Show all work, Do by the indicated method. DETERMINE THE INTEGRALS do by trig substitution.

A: We have to find the integral

Q: Use separation of variables to find the solution to the differential dy 0.3(y – 300) if y = 60 when ...

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Q: Given the interval (a,b), on the x-axis with the point c inside, find the greatest value for 8 >0 su...

A: Finding greatest value of delta...

Q: =) Solve the Initial value problem: + 3y² /x² + 1 = 0, y(0) = 1

A: Use separable variable method

Q: Integrate the ff: show complete step by step soln

A: Given: ∫ cosec43θ·cot 3θ dθ To solve: The given integral.

Q: dx 4. Evaluate cos? ' x (tan x + 1)

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Q: Find the first derivative using the quotient rule for problems

A: We have to find the first derivative of the given function by using quotient rule. 

Q: Let lim f(x)=4. Find lim (- 5') x→10 x→10

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Q: Calculate ?′(7) using the limit definition if ?(?) = ?^2 + 3? − 4.

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Q: (x²+2x +y) dx +(3x3y-x}dy=o

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Q: 1. Air is being pumped into a spherical balloon at a rate of 4 cm3/min. How fast is the radius of th...

A: 1. Given:   The rate at which air is pumped into the spherical balloon = 4 cm3/min   Diameter of the...

Q: H.W 4-Solve the given system of equations by Gauss elimination. 2 305x1 1 40 2 |x2 12 5 4 85 X3 2 10...

A: Gauss elimination can be done by using matrix and then trying to convert the matrix into the indenti...

Q: Q2: Evaluate Sea$cos² (y s) ds.

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Q: Engineering Analysis

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Q: X72 - Is f continumus at xa2 4. X-2 Xくス -2X

A: You have posted multiple questions. As per the instruction, we will be answering only the first ques...

Q: 3-x • The domain of f(x) = is %3D x² -1 1. R/{1} 2. R/{1,-1} 3. R/{-1} 4. (0, c0)

A: Answer

Q: Some students did treadmill workouts, each one running at a constant speed. Answer the questions abo...

A: Given, Tyler ran 4,200 meters in 30 minutes. Kiran ran 6,300 meters in 12 hour. Mai ran 6.3 kilomet...

Q: Select all expressions that can be used to represent the area of the entire patio.

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Q: Calculus Question

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Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE (...

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0        

Q: Let us have the line whose equation is 3 L: x-= y-5 =+ 2 1 Find the points of intersection of the li...

A: given line is                                                              L: x-32=y-5=z7+2  

Q: Vim - seecx メーコ

A: L'Hopital's rule If we encounter with indeterminate form then we differentiate the numerator and den...

Q: 27. (x² + 2x+ y) dx+ (3x²y –x) dy=0

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Q: Find the centroid of the region bounded by y = 4 · x² and y = 3. VI Answer: (ĩ, j) = O (0.371467,1.2...

A: The given curves are y = 4x2; y = 3x.The plot of these curves are:

Q: Look at the picture

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Q: Please answer in full work

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Q: -1 if y= xsin V1-x Find dy 2 dx

A: d(uv)/dx= du/dx + dv/dx  d(u/v)/dx = [v du/dx - u dv/dx ] / v2  

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.