The curve C is the portion of the graph of y = 16* for 0

Q: (+e*)dx e* -In () 3.

A: Given that: ∫(x-1+ex)dxex-ln1xdx

Q: what is the derivative of y=e^-1/2x(C1cos3x+C2sin3x) and evaluate if x=0, y'=8

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Q: Consider the surface given by the equation z - y = x2. Draw a total of at least 3 traces in at least...

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Q: Find the values of 'a' and 'b' that make the following piecewise function differentiable everywhere....

A: We have to find the value of a and b

Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² + x³...

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Q: y = In (sin x²)

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Q: Question 1 A function F is an antiderivative of the function f on an interval I if for all x E1. A F...

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Q: he general antiderivative of a function is also called the. A integrand B arbitrary constant differe...

A: The general antiderivative of the function

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the ...

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: Determine whether the given sequence converges, and, if it does, find the limit. i. An sin () %3D

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Q: 5. What term number contains x* in x' + identifying the exponential pattern on the variable x, ident...

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Q: Find The Area Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

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Q: To improve her handwriting, Hope practices writing the numbers from 1 to 200. How many times will sh...

A: We have considered numbers 1 to 200 in two class. The first class is from 1 to 100 and the second cl...

Q: An airplane moves in the northwesterly at 125 mi/hr relative to ground, due to the fact there is a w...

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Q: Consider the sequence 18 n cos(nn) an 2n 1 Write the first five terms of an, and find limn→∞ an. If ...

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Q: the population of a colony of hamsters grows exponentialy. the colony begins with 10 hamsters five y...

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Q: 3. Find the area bounded by the graph of the indicated equations over the given intervals (when stat...

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Q: Exact Differential Equations (2xy + 1)dx + (x² + 4y)dy = 0 (18) (6xy + 2y? – 5)dx + (3x2 + 4xy – 6)d...

A: First I have written the definition of exact differential equation and it's solution rule, just use ...

Q: Question Suppose that the following functions all have the given limit at a = -1. lim f(x) = 0 lim g...

A: Given that:                  

Q: Use algebra to simplify the expression before evaluating the limit. In particul the highest power of...

A: Given: limn→∞-3n8n7+517

Q: Determine whether the following is always true or not always true. Given reasons for your answers. J...

A: let Vector  u=u1,u2,u3  v=v1,v2,v3  w=w1,w2,w3 

Q: 17. Find the volume of the solid generated by revolving about the x-axis the region bounded by the u...

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Q: Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter...

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Q: Vrite out the first five terms of the sequence with, In(n) n+1 determine whether the n=1 sequence co...

A: We will find the limit 

Q: Question 4 The inventors of Calculus were Sir Isaac Newton and_ A Friedrich Gauss B) Gottfried Wilhe...

A: Carl Friedrich Gauss is known for his contributions to number theory, geometry, probability theory, ...

Q: Use the Pythagoraen Identities to fill in the blanks. 1= 1= :

A: NOTE: Refresh your page if you can't see any equations. . from the right angle triangle, we can wri...

Q: 3. (а) х-ахis (b) y-axis y-4-

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Q: Find g(x)= -x2+ 5x - 2 when g1(2)

A: First calculate g'(x) then put x = 2.

Q: Scscx cotx sin (csc x )dx

A:

Q: f y=x^5, then y’=

A: FOLLOW THE PROCEDURE GIVEN BELOW.

Q: Define function rules f(x) = 2 Vx-1 by using the limit rule f'Cx) lim f(xth) - FCx) %3D

A: Topic:- calculus

Q: Write an equation of the tangent line to the curve f (x) = 3/ Va + 8x at the point (4, f (4)). %3D U...

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Q: If the solution of y' = 2(2x - y) passes through the point (0,1), determine x when y = 7.

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Q: dP 16. dt 11-18 Find the solution of the differential equation that satisfies |Pt, P(1) = 2 7.3: 16 ...

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Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 ...

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Q: Let r(t)=(t+1)i+((t^2)−1/(t−1))j+sin⁡(−2πt)k. Then limt→1r(t)=

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Q: Find the piact farglhofthe Curve ー7 カ+6-6 2ナタナ

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Q: know what the derivative of e^(g(x)) is and what the derivative of In(g(x)) is. I.e. the chain rule ...

A: From chain rule  If g(x) is a differentiable function, then the derivative of eg(x) is g'(x)*eg(x) ....

Q: Find the ABSOLUTE VALUE of the gradients of the tangents drawn to the ellipse x^2/4+y^2/93D2 at the ...

A: We have to find absolute value of gradient at x=2 for the given function.

Q: Consider a circle with equation x² + y² = 20 and the point P with coordinates (-1, 2). Is P inside, ...

A: We have to solve the circle inside, outside, or on circle

Q: y" – 3y' + 2y = 2x² + 1

A: The Solution is given below

Q: given

A: We will solve the integration. 

Q: (a) What is the relative growth rate? Express your answer as a percentage. (b) What was the intitial...

A: Follow the procedure given below.

Q: (You can click on the graph to enlarge the image.) (a) Which one is bigger, f(3) or f(5)? O A. f(3) ...

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Q: Given that f(4) = -8 and f'(4) = –6 , find an equation for the tangent line to the graph of y = f(x)...

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Q: Solve the differential equation (y¯+ y)dx - (y¯+ 2xy + x) dy = 0. If y = 1 when x = 3, determine x w...

A: Topic:- differential equations

Q: 13 – 2r dx 1.

A:

Q: 1. Find the limit of the following: х* — 11x5 + 37x* +6х3 — 297x? + 621х — 405 - lim,-3 А. x→3 x° — ...

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Q: 4. Show that In x lim x→1 x – 1 1. (Hint: Note that In In x-ln 1 x-1 and interpret the limit as a de...

A: Given: To prove that limx→1 ln xx-1=1 using the limit as a derivativeFormula: f'(a)=limx→af(x)-f(a)x...

Q: Given points P(2, 4, 3) and Q(1, -5, 2) in the rectangular coordinate system. What is the resultant ...

A: Given points P2,4,3 and Q1,-5,2  in the rectangular coordinate system.We need to find the resultant ...