Consider the function f (z) = es: Show that if f (z)is purely imaginary, then 2n +1 T, n = 0,±1,±2, ... 16

Q: Find g(x) given that g'(x) = cos x and g(π/2) = 4.

A: Given; g'(x) = cos x and g(π/2) = 4.

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4.x + 2y + z subject to x +…

A: Apply Lagrange multiplier

Q: ind the area under the given curve over the indicated interval. 15) y =ex; [1, 2] 4. 3. 2 A) e2 -e…

A: We have to find the area under the curve.

Q: Determine whether the series converges or diverges. Σ n2 + 5 n = 1 converges O diverges

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Q: Find all solutions to the equation. 2 sinx- cosx=1 Write your answer in radians in terms of t, and…

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Q: Find the general solution of the following differential equations: a. +6- dr + 9 0. dr3 dr² dy + 4.…

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Q: 2. Give the symmetric equations of the line l perpendicular to the plane T : 5x– 2y = z+4 and…

A: we have to find equation of line.

Q: Determine if the sequence {an} converges or diverges. Find the limit Lif the sequence converge. an =…

A: We have to determine whether the given sequence an converges or diverges. Also, find the limit L.…

Q: 1 .! Determine if the vectors 0 and 1 span R³. -2 3 Can these three vectors form a basis for R.

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Q: 1.. Determine the equation of th a) -3 36 -2 26 1 16 1 -4

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: Vr2 – 2x – 3x (x² 4. lim 4x + 5 (72 25) ten2(r1 2)

A: first we will take x common from numerator and denominator, then take limit.

Q: Q/ Evaluate the integrals :- 1 + Z

A: This question is based on indefinite integral.

Q: 2) Find the volume of the solid under the plane z = 3x +y and above the region determined by y = x'…

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Q: 3x2 dx . 4. Evaluate 7x +C 3/1-x cos (3x) + C sin-1(x³) + C The antiderivative cannot be found

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Q: 6 Evaluate the limits lim: X+ co X 6.

A: Topic:-   limits and continuity

Q: On a map, Orlando is 178 mm due south of Niagara Falls, Denver is 273 mm from Orlando, and Denver is…

A: Explained below

Q: The graphs of the first and second derivatives of a function y = f(x) are given below. According to…

A: This question can be solved using the concept of graph of derivatives.

Q: 161 n + e 20 n 2n + tan (103 n). CO The sequence is n=1 O divergent as its limit is o 161 O…

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Q: 2 is a critical number of the function f(x) = /2x – x². Select one: OTrue O False

A:

Q: 1 g(x, y) = cos (Tx VT) + log3(x – y)' Calculate the instantaneous rate of change of g at the point…

A: To solve the following problem

Q: Consider the following. f(x, y) = xy2 4 r= 4 r= 3 (a) Set up an iterated integral in polar…

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Q: Find the slope of the tangent line to the curve given by x + y° = 2 at the point (1, 1) -1 O 1

A: find the slope of the tangent to the curve x5+y5=2 at (1,1)   d(xn)dx=nxn-1

Q: Bacteria grown in a certain culture increase at a rate proportional to the amount present. If there…

A: This question is based on application of diffrential equation.

Q: y = x2 – 7, y = 2x + 10, y = 10

A:

Q: (a) Suppose f is a function with domain the interval (a, b) with a < b. If f is an even function,…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: if x >0 if x = 0. Find f' (0) using the definition of derivatives. sin 4x 3. Suppose f(r) = {0 x* +…

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 1 + (-9) +…

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Q: Evaluate the difference quotient fla + h) - fla) for the function 7+ 3x . f(x)= 4

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Q: -8 dx Se-2-7 10.

A: Solving

Q: 2. S

A: Given :∫xdxx2-4x-7

Q: 31) Find a company's total-cost function if its marginal cost function is C'(x)=5x2-7x+4 and C(6)=…

A: Marginal cost function of a company is given is , C'(x) = 5x2 - 7x + 4  Also C(6) = 260 We have to…

Q: (D2 + 4)V=4 cot 2x

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Q: Using Lagrange multiplier method to find the maximum and minimum value of the function f (x, y) = x²…

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Q: Which formula would be used to calculate the left rectangle approximation of o 4x dx using five…

A: topic - integration using left end points

Q: What is the significance of the fundamental theorems of calculus in the integration process?

A: This is a problem related to calculus. Based on the available concept we will answer the question.…

Q: which of the following polar equations represents a cardioid? -r= 3-2cose r= 4+4sin0 r= 2+3sine T…

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Q: Which of the following triple integrals evaluates the volume of the ssolid that lies above the…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: + 2x-3 Find a lim f) b lim , x) Jig. f(x) d lim rx)

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Q: Find the Laplace Transform of the given function using the definition of Laplace Transform a. f(t) =…

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Q: 5. L.V4– 2x dx dx 5x+2 6.

A: Topic = Integration

Q: workshop grinding at 13.2 ra switch off. Assume the whell constant decceleration n

A: Please refer to the image below

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

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Q: Oyp-3xpy +2x=0.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 3. The price-supply and price-demand equations of a certain product are given by p = S(x) = 15+0.1x…

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Q: We have found the values of t for which v(t) s 0 and v(t) 2 0, so we can write the definite integral…

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Q: Let D={(x,y,2) : x2+y2+z?s 1600, z2 o}. Evaluate - z dv.

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Q: Suppose that f is defined everywhere and 1 are the only critical numbers for f. If f"(x) = 2x + 1,…

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Q: 2x2 If we approximate f(-/4.1,/49.1)' Suppose we have a surface f (x,y) ,which of the following is…

A: I have appended the formula used in the solution part.

Q: V312-x2 31 dydx = %3D 1+x2+y2 Jo int062) ○ 푸n(31) 2 O In(962) O TIn(962) O 2nln(31)

A: Given: I=∫031∫0312-x221+x2+y2dxydx   Now convert to polar coordinate to solve the given integral. As…