Evaluate the limit If the limit does not exist enter DNE. Limit Number = lim x 6 x2 x-6 6 x

Q: Find the length of the curve. 1 10x³' y = 6 + X 2≤x≤4

A: y=x56+110x3,  2≤x≤4

Q: On a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m³, length 88.6…

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Q: a. Graph the functions ƒ(x) = x/2 and g(x) = 1 + (4/x)together to identify the values of x for…

A: Given:-f(x)=x2g(x)=1+4x

Q: Find the limit of each of the following sequences, using L'Hopital's rule when appropriate. √n Vn+1

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Q: Determine the solution of the differential equation: (3tanx-2cosy)sec²x dx + tan x siny dy = 0

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: (7) sin √x dx. (First substitution, then by parts)

A: The solution for the given integral is as follow.

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Q: O D. dependent variable = y, second order, first degree, not linear

A: The given differential equation

Q: Evaluate the following limit: lim O O O 6x²+17x-3 lim x→∞ 5x²+14x-3 6x²+17x-3 lim x→∞ 5x²+14x-3…

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Q: 5. Logarithmic Differentiation Method dy (a) Let y = x. Compute by using logarithmic…

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Q: Find the total area bounded by the graphs of f(x) = 3x³x² - 10x and g(x) = -x²+2x. O 32 units² O 8…

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Q: fxe* dx.

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Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

Q: Which of the equations below is a second order nonlinear differential equation? O B. O A. 2 dy |x²y…

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Q: Let f(x) be the function 9 x² − 3 x + 4. Then the quotient a = Number and b = Number f(4+h)-f(4) h…

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Q: Tutorial Exercise Determine the set of points at which the function is continuous. G(x, y) = In(x² +…

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Q: Evaluate the following integral. dt -1² +8t-15 Rewrite the integrand by completing the square in the…

A: First of all we will solve the denominator then we will solve the integration.

Q: Sketch the region bounded by the curve x² - 2 = y and the line x = y + 2 and find the volume of the…

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Q: 11 Find the derivative of f(x) = -15sinx + +3√√x-5. X

A: Given function:- fx=-15sinx+11x4+3x7-5

Q: lim x→7 x-7 14 x² - 7²

A: SOLUTION-

Q: The limit lim h→0 f(x) a = = In(e +h)-1 h represents f'(a) for some function f and some number a.…

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Q: If f(x) f'(x)= -3x sin²(x) + 3x cos² (x) + 3 cos(x) sin(x) = 3x sin x cos x, find Find f'(4) =

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Q: Write an equation for each line. 15. through (2, 2), y-intercept 10

A: since you have posted multiple questions i can do first question as per our company guidellines.…

Q: Question 2 Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 A. 1/4 B.…

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Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A: The given differential equation is x-ytan-1yxdx+xtan-1yxdy=0

Q: - 4- ن 2+ ا ? " ? تان 4. - At each of the following points, choose the selection that best describes…

A: We have to find the nature of continuity at the given point according to the given information

Q: If y=f(x)=7e^x + 3x^4 - 20x - 5 , Find the x-intercept of the tangent line at x = 0 to the graph of…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Determine the degree, order, and whether it is linear or non-linear (y") ³-4y²=105x

A: Determine the degree,order, and whether it is linear or non linear

Q: True or False The slope of a nonvertical line is the averagerate of change of the linear function.

A: The average rate of change of the linear function is the slope of a nonvertical line.

Q: 7. Find (a) the slope of the c y=9x² -1; P(4,143) (a) The slope of the curve (Type an integer or a…

A: solution:-y=9x2-1slope= dydx=ddx9x2-1=18x(a)slope of tangent at point P(4, 143)slope = 18(4)=72

Q: Integrate. S2x² sin (12x) dx = +C

A: Given query is to find the integral.

Q: Use the first derivative test to determine all local minimum and m points of the function y=x³-6x²…

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Q: Derive a Differential Equation that is free from arbitrary constants: y = Ae²x + Bxe²x

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Q: Suppose Use this to compute the following limit. Limit= Number What Theorem did you use to arrive at…

A: Snadwich TheoremSqueeze Theorem:  If g(x)≤f(x)≤h(x)  for all x in an interval containing a point…

Q: If ƒ(x) = 8x¹¹(»), find f'(8).

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Q: A population of bacteria is growing according to the equation P(t) hours. Estimate when the…

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Q: Given the differential equation: 2 y' + ²y = 6x²

A: To choose the appropriate method to be used to solve the given DE. Method 5: Exact Equation Method…

Q: In 2004, an art collector paid $59,886,000 for a particular painting. The same painting sold for…

A: To find out the exponential growth rate and also the exponential growth function.

Q: Suppose f f(x) dx = 25, f f(x) dx = 10, f g(x) dx = 10 and h(x) = 0 3 the following: a. (5f(x) 6g(x)…

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Q: 8. Find the limit of f(x) = lim f(x)= 4- 818 (Type a simplified fraction.) lim f(x) = 8118 (Type a…

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Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Condition for existence of limit at x=a⇒limx→a-fx=⇒limx→a+fx=⇒limx→afx

Q: Points A and B are separated by a lake. To find the distance between them, a surveyor locates a…

A: Given query is to find the distance between A and B.

Q: 5x2+x+4 2 (x² + 2)(x − 6) – dx =

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Q: An offshore oil well is 5 kilometers off the coast. The refinery is 4 kilometers down the coast (see…

A: Solution

Q: Consider two lines. Line L1 is defined by 1, and Line L2 is defined by y = 3x y = 2x + 4. A. Without…

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Q: The linear trend forecasting equation for an annual time series containing 45 values (from 1963 to…

A: Given     Yi^ = 4.8 + 1.3Xi As per the student's request, I am providing the solution to the (c)…

Q: graph each function using the techniques of shifting, compressing or stretching, and reflections.…

A: Given, hx=2x-1

Q: 7x - 4 3 – – 4x 4x² dx

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Q: (b) Let y = (2x + 1) cos. Compute by using logarithmi dy dx

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Q: Find the present value of $6000 payable at the end of 3 years, if money may be invested at 8% with…

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