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Q: Find the fifth term in the expansion of (2x + y)9.

A: 2x+y9 Comparing with a+bn, we get a=2x, b=y & n=9

Q: Factor the polynomial completely. P(x) = x3 + 25x P(x) =     Find all its zeros. State t...

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Q: Evaluate the line integral 11y dy over y = x for 0 < x < 3. (Use symbolic notation and fractions whe...

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Q: Co. 2. DEvalKate 20-2x-3

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Q: 3. If f(3) = 2 and f'(3) = -4 , find an equation of the tangent line when x = 3. %3D %3D А. у%3D2 (х...

A: Given : f(3)=2f'(3)=-4

Q: Determine whether the series is convergent or divergent. 1 1 1 1 1 + + 2/2 3/3 4V4 5/5 The series is...

A: Given : 1 + 122 + 133 + 144 + 155...

Q: I am having trouble setting this up

A: Formula of area of triangle 12bhWhere b is the base and h is the altitude Chain rule (uv)'= u'v+uv'

Q: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3, and...

A: Given zeroes of polynomial are 0 and i.    

Q: 6) Write a polynomial function whose graph is shown (use the smallest degree possible). 100 80 60 40...

A: Given that: The graph  To find: Polynomial function for the given graph.

Q: 14)Find a polynomial function f with real coefficients having the given degree and zeros. Degree: 4;...

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. x + 10x + 2...

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Q: At which points on the curve  y = 1 + 40x3 − 3x5  does the tangent line have the largest slope?

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Q: For f (x) = (x – 4)³(x + 3)²(x - 5) determine the following: a. List each real zero and its multipli...

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Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder incre...

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Q: Integrals using trigonometric substitution Perform the following indicating integrals. 2. ∫ dx/x sqr...

A: We have to evaluate the integrals using trigonometric substitutionand to perform the indicated integ...

Q: 4. Use the exponential shift to find the general solution. (D – 7)*y = 0

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Q: *indefinite integral* 2tan4(x)sec6(x)dx

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Q: if none of the choices represents a correct answer, select the option “Other” and write your own ans...

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Q: Consider the following function on the given interval. f(t) =2 cos(t) + sin(2t), |0, 프 Find the deri...

A: We find f'(t) using the chain rule f(t)=2cos(t)+sin(2t)f'(t)=2(-sin(t))+cos(2t)ddt(2t)f'(t)=-2sin(t)...

Q: Find the absolute maximum value of y=sqrt(16-x2) on the interval [-6,6]

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Q: Problem 2: I love those Swedish fish, especially the red ones. My Swedish fish box has broken, so we...

A: Given- Volume of cylindrical can is 1000 inch3. To find- The surface area of the can as a function o...

Q: need help please  I always have trouble with the negative ones.  The measure of an angle in standard...

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Q: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

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Q: ) Find the differential of f(x,y)=x3+y2−−−−−−f(x,y)=sqrt(x3+y2) at the point (1,2).df =  Then use th...

A: Given: The function fx,y=x3+y3 and the point 1,2 The differential to estimate f(0.94,1.94).f(0.94,1....

Q: Use the Integral Test to determine whether the series is convergent or divergent. n°e-n5 n = 1 Evalu...

A: Given, ∑n=1∞n4e-n5

Q: If the revenue function for a certain commodity is R(x) = 45x/lnx compute the marginal revenue when ...

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Q: i sin (æ). Click and drag the highlighted points to shift Graph the function y = the graph and to ad...

A: If y=AsinBx+C+D Then Amplitude = A Period = 2πB Phase shift = C Vertical shift = D

Q: Let ƒ(x) = (x - 3)(x + 3)2.a. Verify that ƒ'(x) = 3(x - 1)(x + 3) and ƒ"(x) = 6(x + 1).b. Find the c...

A: Given that, f(x)=x-3x+32

Q: Shift + Mouse Wheel to zoom. X Shift + Mouse Drag to pan.

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Q: Write a polynomial function whose graph is shown (use the smallest degree possible). 100 80 60 40 20...

A: It is given that, the graph of the polynomial function touches the x-axis  at x=-3  and intersect at...

Q: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/...

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Q: Given the graph of f(x) in the figure, what are the x-coordinates of the local extrema? Enter your a...

A: The graph of f(x) is as shown below :

Q: 19) Determine if the following functions are inverses of each other. State any restrictions on the d...

A: f(x)=2x2+3g(x)=x-32 If f(x) and g(x) are inverses to each other then f(g(x))=g(f(x))=x Now we find f...

Q: One solution of the differential equation is given. Find the general solution. y(3) + 2y" + 10y' - 1...

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Q: 5. Which one of the following equals |(1+ 2x²)e*´dx? a(*+( A. 2 ,3 3 O B. xe*“ C. e ( ? ) =* + z 2 С...

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Q: Graph t(x) = (x – 2)3 + 1 by starting with the graph of y = x3 and using transformations.

A: Compare the function tx=x-23+1 with its parent function y=x3, to identify the transformation of the ...

Q: Please help with problem attached.

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Q: 6. The half-life of cesium-137 is 30 years. Suppose we have a 378-mg sample. Find the mass that rema...

A: Given data: The half-life of cesium-137 =30 years The general equation of decay is given as: Pt=P0ek...

Q: (d6/dx6)(x2 sin x)

A: Given function is fx=x2sinx    

Q: C(x) = 5x;  R(x) = 9x − 0.001x2   Calculate marginal cost, marg revenue, and marginal profit. then, ...

A: Given data:   The expression for the cost function is C(x)=5x. The expression for the revenue functi...

Q: What would be the rate of increase of an island population of 1000 that has 30 births and 20 death? ...

A: An island population of 1000 that has 30 births and 20 death. We need to calculate What would be the...

Q: What is the net signed area between f(x)=2x+2 and the x-axis over the interval [−8,5]?

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Q: Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider...

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Q: Find the equation of the tangent line to the curve y = 4 ln at the point (1, 4). (Hint: simplify bef...

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Q: Find the focus and directrix of the parabola with the given equation x2 = 8y. Then graph the parabol...

A: we have to find the focus and directix of the parabola with the given equation x2=8y. then we have t...

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.