Write the sum 5 + 15 + 45+ + 1215 using sigma notation. ... a1(1 – r") - Then evaluate the sum using the formula Sn 1 - r Σ n =

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A: Compound interest

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A: Given:        y  = 3x2-4x+2

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

A: we have the following antiderivative formulas∫cosx dx=sinx+C∫secx tanx dx=secx+C∫sinx…

Q: The limit lim cos is an indeterminate form of type 0· o. 00. Select one: O True False

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Q: Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9)

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Q: The limit lim (x In( cos x-00 is an indeterminate form of type 0 0o. Select one: True False

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Q: Assuming annual compounding, find how long it would take for the general level of prices to double…

A: Given query is to find the time taken to double the amount.

Q: 1. Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find a corresponding…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. do r= 6 e a0 and -= 3 dt Ju, +Juo

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Q: 12. Find the profit function for the given marginal profit and initial condition. dP = -40x + 290,…

A: Solve the following

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A: Explanation of the answer is as follows

Q: S tan“ x sec“ x dx

A: Given query is to find the value of the integral.

Q: Find the following limit. Answer in either integer or fraction form. NO DECIMAL APPROXIMATIONS. If…

A: Use l hospital rule for finding the limit.

Q: Q2 Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x =…

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Q: Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y…

A:

Q: kt Convert the equation f(t) = 310(1.13)' to the form f(t) =

A: answer is in next step

Q: Write a in the form a = a-T+aNN at the given value of t without finding T and N. 3 (5 e'V5)i+…

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Q: 15 lbs 200 27° 12 lbs What is the approximate magnitude of the resultant.force? A 22.2 pounds. 24.8…

A: using component

Q: Determine the local maximum and minimum values and the saddle points of the function: f(x,y)…

A: Given, f(x,y) = y3 + 3x2y - 6x2 - 6y2 + 2

Q: Evaluate the integral. 1/2 | [6 cos ti-3 sin tj+ sin 3t k] dt 1/2 | (6 cos ti- 3 sin tj+ sin? 3t k]…

A:

Q: 12 Consider the graph of the ellipse. which is drawn to scale. This ellipse has an eccentricity of…

A: Given query is to find the equation of the ellipse.

Q: 2. Find the volume of the solid bounded by z = 0, x = y2,z= 3, x = 4 - y2. (graph the solid)

A: Given problem:- Find the volume of the solid bounded by z = 0, x = y2 ,z= 3, x = 4 - y2

Q: ² f r' రy2 Əx? dy? dz? x² + y? + z²

A:

Q: If va + Vỹ = 12 and y(4) 100, find y' (4) by implicit differentiation.

A:

Q: Q2: Evaluate o o" y*(x² + y²)dx dy 1 cV1-y? y² (x? + y?)dx dy

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Q: To find two real numbers whose difference i and whose product is minimum, we can find minimum value…

A: Topic:- calculus

Q: What is the first term of the Maclaurin expansion of y = 8 e -0.5t cos t?

A:

Q: 7. Let f(x) = -3x + 9x - 3. a. Determine the x values where f"(x) = 0. b. Fill in the table below to…

A: In this question we have to find first three subpart.

Q: 13. The distance s, in metres, fallen by a skydiver t seconds after jumping (and 160(:1 – 1 + e-5.…

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Q: Exercise 4 * Suppose the following data points are generated by a smooth function f(x): 1/6 1/3 1/2…

A: We have to find best approximation using the composite Simpson's rule.

Q: 1- x² tx

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Q: A tire swing attached to a tree branch swings with an arc length of 40 feet on its first swing. On…

A: Question- A tire swing attached to a tree branch swings with an arc length of 40 feet on its first…

Q: Find the volume OF the solid obtained by rotating about the y- axis the region bounded by Y= x2 and…

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Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

A: Solution is done in step 2

Q: Consider the function  f(x,y,z) = sqrt(xyz)   what is the gradient of F?   Determine the…

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Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x -1 X-1 a. Find lim f(x) or…

A: This question is related to limits, we will solve it using given information.

Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: f(x) = 8 cos Tx

A:

Q: Question 1 Determine the inverrse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9)

A: L-11s-a =eat L-1as2+a2=sin(at) and L-1ss2+a2= cos(at).

Q: Classify the statement as either true or false. If f is continuous at x= 2, then f(2) must exist,…

A: Given query is to find statement is true or false.

Q: b). Using gamma function, evaluate Sx6 e-2x dx

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Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: 12. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 f/sec. Assume the…

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Q: Determine the antiderivatives of the following functions: 1. V36-x² dx 2. 9x²+36dx

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Q: 4. Find the Linearization of f (x) = sinx at a 5. Provide your answer as L(x) =? %3D

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Q: se' z = st. Solve for dz IV. Let w = x ln x + 2xyz + 5z°y, x = tan s + r, y =

A: Given problem:- Let w = xln(x3) + 2xyz + 5z3y, x = tan s + r, y = (set )/r, z = st Solve for partial…

Q: Given the function f(x) = -xr* – 4x determine its critical points and classify them, determine the…

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Q: (1 - cosx) dx Evaluate: cosx(1 + cosx)

A: