Differentiate: e6x² A) 6e6x²-1 D) 12xe*-1 B) e 6x² E) 12xe6x² C) 2ex-1 F) 12xe*

Q: g(t) = -tan² (2+) +sin (3+¹+8+³) [[// (++1)]] cot " (cosh (3+1)), ift 71 if t <0 ifo≤t≤1

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Q: the cable of a suspension bridge hangs in the form of a parabola. the distance between two towers is…

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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: 3. Elimination of Arbitrary Contants 1. y = peax cosbx + peax sin bx 2. y = C₁x + c₂ex ; a and b are…

A: Here we have to eliminate the arbitrary constants of the equation y=ϕeaxcosbx+ψeaxsinbx…

Q: the ideas presented in this section, what do you think is thearea under the curve of y = 2- x…

A: Given:curve is y=2-x we have to find the area under the curve bounded by x-axis and x=-4.we will use…

Q: Find the slope of the tangent line to the curve f(x) = x³ - 4x at the point where x = 0. A) 0 B) - 4…

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Q: Find the limit, or show that it does not exist. 2x - y lim (x,y) (0,0) y + x²

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Q: Use algebra to rewrite the expression BEFORE you differentiate. 8x¹7 - 2x¹4 14 x11 A) 32x³ - 2x D)…

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Q: Evaluate S9 cos √2x dx using a substitution followed by integration by parts.

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Q: Find the exact length of the curve. 1 y² = 16(x + 1)³, 0≤x≤ 3, y>0 109/109 (217 217 (21717 X

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Q: Evaluate the following integral using trigonometric substitution. S dx (x²-36) 3/2 " X>6

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Q: Which of the following equations has a solution of the form F(x,y)= A. 2x + 3y + (2y + 3x) dx = 0 dy…

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Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy + 2y)dx + (2y³ + 2x²y + 2x)dy…

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Q: The total cost in dollars of producing x lawn mowers is given by C(x) = 4,000 + 90x - x2/3 . Find…

A: NOTE: Refresh your page if you can't see any equations. . the given cost function is the average…

Q: Find the value of the constant b that makes the following function continuous on R. 8x - 26 f(x) =…

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Q: Question-Solution-Final Answer-Conclusion format) - Generate solution of the first-order…

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Q: Draw the following intervals on the number line. 1. [ -1, 4] 2. (4, 3p) 3. [ -2, 12) 4. [1, 32] 5.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Given half life of 34 hours Initial does of 75 mg

Q: Elimination of Arbitrary Contants 1. y = peax cosbx + yeax sin bx 2. y = c₁x + c₂ex ; a and b are…

A: we need to eliminate the arbitrary constants C1 and C2

Q: A car sharing service offers a membership plan with a $30 per month fee that includes 10 hours and…

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Q: A distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1. Find the…

A: Given that a distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1 .

Q: Evaluate the following limits, making sure to justify your calculations as much as possible: lim…

A: See this solution in below.

Q: Which of the following equations can be made into a linear differential equation? A. (x² + xy)dy -…

A: On solving this we will get

Q: which is what in decimal form?

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Q: Graphing a Linear FunctionGraph the linear function f1x2 = - 3x + 7. What are the domain and the…

A: Given, fx=-3x+7

Q: Solve for the value of C in the equation: A. 1 B. 2 C. 3 D.-1 (2xy4e³ + 2xy³ + y)dx + (x²yªe¥ − x²y²…

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Q: What is the integrating factor of (1+x)y +2y= 21ax sin.x 1+x

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Q: Find the given limit (x² - 1)(y² - 4) lim (x,y) →(1,2) (x - 1)(y-2)

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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: Use the formula for nPr to evaluate the expression 8P0.

A: Given: The given expression is:  8P0 Formula Used: Prn = n!(n-r)!

Q: Find the following limit. lim x-x 2+ x - 4x³-4 5 x³x²+1 Number

A: ans=  -4/5

Q: Shown below is the graph of the flow rate f(t) of a pipe, in gallons per minute. Here, t= the number…

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Q: Find a unit vector in the direction in which f(x, y) = 8 cos(3x − 5y) ㅠ P(20), and find the rate of…

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Q: Generate differential equation by elimination of arbitrary constants. 2. y=x+c₁e* + c₂e-*

A: Given: Now,    y'=x+c1ex+c2e-x' =1+c1ex-c2e-xy''=x+c1ex+c2e-x''=c1ex+c2e-x

Q: According to one model that takes into account air resistance, the acceleration a(t) in m/s" of a…

A: Here is the solution:

Q: The function s(t) describes the motion of a particle along a line. s(t) = t3 − 7t2 + 6t   (a) Find…

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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 following equations can be made into a linear differential equation? OA. (x² + xy)dy -…

A: Option D

Q: Find the directional derivative of f at the point P in the direction of a. P(4,0); f(x, y) = 4x³y³;…

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Q: 7) Find the horizontal asymptote, if any, of the given function. 2x³-3x-9 f(x) 9x³-5x +3 A)y=5 8) If…

A: Here we have to use the concept of limits

Q: Consider the function f(x)=eXx. Select all that apply. Select 3 correct answer(s) f(0) is positive.…

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Q: Let F(x)=f(f(x))=f(f(x)) and G(x)= (F(x))2 and suppose that f(6)=7, f(7)=2, f′(7)=3 ,f′(6)=8 Find…

A: As we know that for composition of function F(x)=ff(x), F'(x)=f'f(x)×f'(x)

Q: Determine the slope and y-intercept of the graph of 3x - 5y = 30.

A: The given equation: 3x - 5y = 30 To determine: The slope and the y-intercept of the given equation.

Q: Find the area between the curves (Hint: Your answer will be in terms of a.) The area is f(x)=x and…

A: area is=a3/6

Q: Find a polar equation for the curve represented by the given Cartesian equation. x + y = 4 2√2 sin…

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Q: Find all the critical numbers of f(x) = 2x4-4x³+3x²+2, then determine the local minimum and maximum…

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Q: Devise an exponential decay function that fits the given data, then answer the accompanying…

A: Here, the equation used is: P=P0ekt...(1) where P is the pressure of the atmosphere at t=0 and k is…

Q: Find the numbers at which g is not continuous. Justify using the definition of continuity. x+2 if x…

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Q: Use limits involving to to describe the asymptotic behavior of the function from its graph. (If an…

A: From graph f(x) goes towards 1 at left end of graph

Q: A community skating rink is in the shape of a rectangle withsemicircles attached at the ends. The…

A: Given data, The length of the rectangle given is 20 ft less than twice the width. The thickness of…