15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex is valid complex values of x to prove the famous, and unbelievably useful Euler identity eie = cos 0 + i sin 0

Q: 2x³ − 45x² + 300x + 6 has one The function f(x) = 2x³ local minimum and one local maximum. This…

A: Given: Axis interception points of 2x3-45x2+300x+6:  X Intercepts: -0.01994…, 0, Y Intercepts: 0,…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 200…

A:

Q: 7- (a) If a is a constant and cannot be equal to 0, find the critical points of f(x) = 3a + 6x (b)…

A:

Q: The force of magnitude F-108 lb acts along the edge of the triangular plate. Determine the moment of…

A: We have to find moment value for the given force.

Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the…

A: Here we have to choose the correct option.

Q: 2 z² +4 lim z 2i 2z²+(3-4i)z-6i

A:

Q: T/6 6 tan 2x dx

A: In this question, we need to evaluate the given integral.

Q: integrate using partial decomposition (y^2)/(y+1)^2(y-1)

A:

Q: P1: Calculate the area bounded by the curves: C. y e* and x - 2y + 5 = 0, and y-axis.

A: To calculate the area bounded by the following curves.y=e-x and x-2y+5=0, and y‐axis.

Q: 4 f(x) = 3x6 3 f(x) = $/x2

A:

Q: f(secx tan² x) dx

A:

Q: Using the definition, find the derivative of function 2z-i 1 (z)= at the point z = = -¡. z + 2i

A:

Q: For the following integral, reverse the order of integration and evaluate the integral. 1/8 1/2 S S…

A:

Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve y =…

A: Given curve, y=5x from 0 to 4

Q: 5- Evaluate: f Sin (2x7 - 3) dx x6

A:

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate…

A: We have to find the series is convergent or not and find the sum also.

Q: Consider the following. [u-5(6 - u³ +4²0) du Simplify the integrand by distributing u¯5 to each…

A: We know that integration power rule is given as - Integration of xn is xn+1/n+1 +C ; here C is…

Q: H.W: show that the equations are homogeneous and solve: 1. (x+y)dy + (x - y)dx=0

A:

Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Find the rate of change of the volume (V) of a sphere with respect to its radius (r) when r = 4. 4π…

A: You must have idea about basics of derivatives. The rate of anything is basically the derivative…

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: Let's solve.

Q: For the function z = = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

A:

Q: Write the first five terms of the sequence: {√n² + 2n = n}=1 Determine whether the sequence…

A:

Q: A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material…

A: Given problem:- A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup.…

Q: Taika invested a total of $ (a+b+c+ 900) × 1,000 into three investment accounts, paying 3%,4%, and…

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Q: As shown in the required readings or videos use a power series to find a general solution to Airy's…

A: Given : Airy Equation : y"+xy=0

Q: Question 4 (a) Solve the following: (b) Explain with the aid of a sketch how this value can be…

A: Above question is solved.

Q: Investigate if the integral is convergent or not. Justify your answer.

A:

Q: Consider the following initial-value problem. f'(x) = 8ex − 4x; f(0) : = 13 Integrate the function…

A:

Q: Solve for the volume of the solid generated by revolving about the y-axis the area under y x = 4 to…

A:

Q: 1. f(x) = 4x² (8x + 1) 2. f(x) = (100x² + 25x)(10x² − 15x) 3. f(x) = (2x + 1)(4x + 3) (5x - 1)

A: Let's solve all given derivative by using product rule.

Q: * ?What is the z-transform of the following finite duration signal x(n)-(2,4,5,7,0,1)? x(z)=2+ 4z…

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Q: lim,+1+(1²-2-²-1) In

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Q: 1. Siste dx It sex x

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: * The z-transform of a signal is given below,its final value z¯¹ (1 - z-4) x(z) = 0.25 (1-z-¹)² 10…

A:

Q: Six 2 CSC ² 2x - x cos 2x) dx

A: We know, ∫cosmx dx= sinmx/m  ∫sinmx dx= -cosmx/m  ∫cotmx dx = ln|sinmx|/m  ∫csc²mx dx= -cotmx/m…

Q: 31. The function fƒ: R→ R is defined by f(x) = (a) Show that f is a bijection. (b) Determine f¹(x) x…

A:

Q: 4. A triangle has sides of length 13 cm and 22 cm and has an area of 100 cm² a) Use Heron's formula…

A: We have to solve the side and angle of given triangle.

Q: Consider the function f(x) = 4 - 5x², −5 ≤ x ≤ 1. The absolute maximum value is and this occurs at x…

A: The given function is: f(x)=4-5x2 To find the absolute maximum and minimum of the function on -5≤x≤1

Q: The diversity of a population that contains two species can be measured by the Gini-Simpson…

A: The diversity is given by H(p)  H(p) = 2p(1-p)   H'(p) = d/dp(2p(1-p)) H'(p) = 2(1-p) -2p H'(p) =…

Q: 2 S² T ㅠ 1-cos x dx 2

A:

Q: Use - -1-1(x Let f(x) = 9x +7 In (x+1), x>-1. Find - dx (Simplify your answer.) x=0 to find the…

A: By using ddxf-1x=1f'f-1x to find the derivative of the inverse at the indicated point. Let fx=9x+7…

Q: 3) (11x + 17) dx 2x² + 7x - 4 S

A:

Q: Evaluate: lim 1+ O 1 a 00 none of the choices In aª (A)

A:

Q: 1) e5Ln x+4Lny-Ln z 2) 2Ln√x+2Lne√ - 2Lne* QV² + 2²

A:

Q: 12) The formula of the particular solution yp of y(4) + 4y"=3 sin(2t) - 5cos2t, is: a) yp= Asin(t) +…

A: The given differential equation:y4+4y''=3sin2t-5cos2t.We need to find the formula of  the particular…

Q: 9) Ур H Asin(2t) + Bcos (2t) Q13) The general solution for y' a) = 3x² + c b) = y Q14) The solution…

A:

Q: Q1) L-1 s(s a) cosht -1 b) 1-cosht c) (cosh2t - 1) d) (1 - cosh2t)

A:

Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 20 cm. Answer:…

A: Find area of largest rectangle that can be inscribed in a circle.of radius 20cm