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Q: 1. Write z = -6+ ót in polar form. O z 6 V2 cos-+i sin 4 4 = 2/6| cos- +i sin- 4 O z = 6 /2 cos…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4ay = x2, and y = x + 3a

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Q: x*-y* 3) x²y³ = **-y+ ху

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Q: The two planes given below intersect along line l. Determine the distance from point P (2, 3, –1) to…

A: This question can be solved using the concept of line and plane in three dimensional geometry.

Q: In Exercises 31 and 32, find the unit vector having the same direction as V(P,P,). 31. P;(4,–1,–6);…

A: To find the unit vector that lies in the same direction as V.

Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

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Q: 2) y = 3tan 3 - -2 3n 27 5n 3n 7 47 9n

A: Given query is to graph the function.

Q: 1 1+x3

A: ∫11+x3dxSince a3+b3=(a+b)(a2-ab+b2)∫1(1+x)(1-x+x2)dx

Q: 2 fcx) = x ニX +2 -100 Solve this question by the Newton-Raphson method on the topic of solution of…

A: This is a problem of numerical method. Based on the general formula of solution of algebraic and…

Q: Determine where the function is concave upward and where it is concave downward, (Round your answers…

A: Solve the following

Q: Find the terms through degree 4 of the Maclaurin series of f. Use multiplication and substitution as…

A:

Q: Find the absolute maximum value of f(x) = x² - 2x +9 over the interval [0, 5] |

A: Given problem:- Find the absolute maximum value of f(x) = x2 - 2x + 9 over the interval [0,5]

Q: Evaluate the tolloW ing limits と-1

A: =limx→1  x-1x2+x-2=limx→1  x-1x2+2x-x-2=limx→1  x-1x(x+2)-(x+2)=limx→1  x-1(x+2)(x-1)=limx→1…

Q: 4 Using the e – 8 definition of limit, prove that lim x→3 3x 1 1 2

A: To prove the limit of given function using the epsilon delta definition of limit which states that…

Q: Show that the quadrilateral having vertices at (1, –2, 3), (4, 3, –1), (2, 2, 1), and (5, 7, –3) is…

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Q: Find the derivative of the function. h(x) = log4(x + 9) h'(x) =

A: Topic = Derivative

Q: | (5e" + 5a* + 9cos r+ 2)dr O e* - a5 + cos a + 2 + c O 5e" + a -9 sin a + 2+ c O e +a5 - 9 sin z +…

A: Here we have to evaluate I=∫5ex+5x4+9cosx+2dx

Q: Find the absolute maximum value of f(x) = x2 – 2x + 10 over the interval 0, 3 -

A: Find your answer below

Q: The value C for the solution of the initial value problem f'(x) = x - 8 +4, given that f(0) = 0. %3D…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Note: Below we are using t as the variable for angles instead of 0. 1 Consider the following…

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Q: Needed

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Q: pressions without using a b) log, (log, 125) d) (log, 128)(log4 256) f) log, 82 – log, 49 + log, 1…

A: We have to solve the logarithmic expression.   According to our guidelines we can solve only three…

Q: + 16)° dx

A:

Q: A builder must fence all sides of 3 adjacent rectangular lots, each having 168 m2 of area. Front…

A:

Q: xsin-1x dx V1-x²

A: Given

Q: Let f be the function defined as follows. 10x2 + 2 y f(x) %3D X + 3 (a) Find the differential of f.…

A:

Q: (8) Let /(x) = In(1 + 36x²). (a) Find the Taylor series for f centered at a = 0. (b) Show that the…

A: Solve the following

Q: х—1 ]dx x4 -1

A:

Q: 1 S dx 1+x3

A: First we take partial fraction.

Q: Answer the following True or False. Let f(x) be a continuous increasing nonnegative function. Then…

A: Let f(x) be a continuous increasing nonnegative function.Then the left endpoint Riemann sum…

Q: A table of values for f, g, f ', and g' is given. f(x) g(x) f '(x) g'(x) 3 2 4 2 1 8. 7 3 2 9. (a)…

A: Consider the table

Q: (3e² + 5æª + 6 cos a + 2)dx : 3e? + x + 6 cos a + 2x + c 3e + a + 6 sin a + 2x + c et - x5 + cos z +…

A: Given problem:- ∫ (3ex+5x4+6cos(x) +2) dx

Q: You construct an open box with locking tabs from a square piece of material, 24 inches on a side, by…

A: Solution is here

Q: nd d²x/dt² as a function of if 4 = 7x sin x.

A: Given query is to find the derivative of the the expression.

Q: 1 dx 1+x3

A:

Q: Evalua fe the integral 7) Of xy dx sübjcct to the functional relation X = at and

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Q: Find the absolute maximum value of f(x) = x? 2x + 12 over the interval [0, 4] -

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Q: The antiderivative of the function f(æ) 6. + 8x is. -6 + 16.0x? + c -6 4.0x? + c 6 + 4.0x² + c -6 +…

A: We have to find the antiderivative of the function f(x) = 6x2 + 8x

Q: х—1 dx х4—1

A:

Q: 30 cm of wire is cut into 2 pieces. One piece is bent into a square, and the other piece is bent…

A: To find out the length of the two pieces.

Q: find the second derivative for the following parametric equation x = e-t y = te3t find the…

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Q: 2) Vy + 2x = (e – 1)3

A: Given query is to find the derivative of the expression.

Q: Evaluate: (20t3 – 12t? + 7)dt

A: ∫03 (20t3 - 12t2 +7 )dt here we use rule of integration xndx = xn+1/(n+1) [20t4/4 -12t3/3 +7t]03…

Q: 'ax+b 1) g(x) ) (a and b are constants) = sec ax-b

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Q: When estimating distances from a table of velocity data, it is not necessary that the time intervals…

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Q: Solve equation by using the quadratic formula. List the solutions, separated by commas. 3t + t – 9 =…

A: Our Aim is to solve equation given below using the quadratic formula3t2+t-9=0 -(i)

Q: The value C for the solution of the initial value problem f'(x) = x* – 8x + 4, given that f(0) = 0.…

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Q: 3 dx x² +4x+29

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Q: Solve the system of linear equations and check any solutions algebraically. (If there is no…

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Q: Determine the area bounded by

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