Use the Chain Rule to find dz/dt. z = sqrt 3+ x^2+y^2, x= 3 ln t, y= cos t

Q: In the last 4 line, where is the ^2 in the ln part?

A: The given integral,      ∫13arctanx dx

Q: Let i denote the square root of-1. For the two complex numbers =3e and w= 6e find 2, w. Grve your…

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Q: (i) What are the projections of the point (2, 3, 5) on the ry-, yz- and rz-planes? (ii) Write…

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Q: (-1)" „2n for all x E R. (2n)! Consider the series expansion of the cosine function cos(x) = > n=0…

A: nth degree Maclaurin polynomial for f(x) :       f(x) =∑ i=0n fi(0)i!xi   =…

Q: 3. dx

A: Integral CalculusExtension of power formula

Q: イナ dx メーよ

A: Given :∫12x+1x-5dx

Q: An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per…

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Q: 3) solve: y'-Hef't 44=HC032t; y0)=2, qla)== using Laplace treensform |

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Q: 2x lim

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Q: Differentiate exp(sec(x^2)

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

Q: fex) = I+ sinu x f(x) = 1T fcx) =-15 * sinux - secos4X %3D = -15 e sin4X- se"cos4X mL

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Q: 4. S(x² – 1) Vx + 4 dx

A: Solving

Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x –…

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Q: please can you also answer number 3.

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Q: Simplify arcsin(sin240°). 60° 240° -60°

A: First draw the grap then make all the point then simplify.

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: 5. f(x) = 2x + 3

A: First write the formula and then put all the values and simplify.

Q: Evaluate the following integrals. Use only the variables "u" (and "v" if applicable) in your…

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Q: A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle.…

A: Explanation of the answer is as follows

Q: dx The integral of the given function S is equal to (x²–2x+4)ž а. 1/4 b. 1/5 с. 1/6 d. 1/3 e. None…

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Q: What is the volume generated by revolving about the x axis the area bounded by the y = 2x + 1, y =…

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Q: Please clarify the answers.

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Q: Xv16+x dx

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Q: 2" n3 Σ 4"+1 n=1 is convergent or divergent.

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Q: how is the irrational zero found?

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Q: 2) solve: 4-Hy+34 using the unde ter mined coefficieuts methed = 20 cosX

A: Solution is given below:

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATION 1. (D^3 – 3D^2 – D + 3)y = 0

A: The given differential equation is: D3-3D2-D+3y=0 So, the auxiliary equation is: m3-3m2-m+3=0

Q: What are the local extreme values of the function f(x) = x - 3x² + 2?

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Q: 3. Evaluate: lim -) X-0 \sinx 4. Using the binomial series, find the power series of f(x) = =

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: 1. Solve the initial value problem 2 = x? – 1, y(3) = 7. dx

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

A: We need to find the slope and the equation of the tangent line tothe following curve:3. y=3x2+2 at…

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

A: The graph of the first and second derivative of the function y = fx is The statement is f is…

Q: v5-x dx

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Q: Let i denote the square root of – 1. For the two complex numbers z = 3e and w = 6e'5 find z. w. Give…

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Q: Consider the function f(x) = x2-1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: 4. Find the absolute extrema (abs. max and min) of f (x) = x2 - 8x - 1 on the interval [1, 10].

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Q: e definite integral o5 tan(x)dr using strips of width for the trapezium rule correct to three…

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Q: 3. Find the number in the interval ,2] such that the sum of the number and its reciprocal is (a) a…

A: Let number = x,  It is given that, the function is = sum of number and its reciprocal

Q: The answer is not -900. Please give me the correct answer.

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Q: 44 3) y" +y = sec?x (Use variation of parameter method)

A: To solve the given differential equation.

Q: Find T(t) and N(t) at the given point. r(t) = (t – 2)i + tj; t = 2 4 i+j T(2) : V5 N(2) = i

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Q: please use the method of Miscellaneous Substitution

A: Here  We will use miscellaneous Substitution instead of partial fraction.

Q: Consider the function f(x) = x2+1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: Evaluate the difference quotient for 7x+1. Az) - f(x) = 2 7/2 7 O 1/2 O O

A: Here we have to find the quotient difference of a function.

Q: For the following function, find its inverse. f(x)= In(8x – 9) O a. f'(x)= (e* - 8)/10 O b. f'(x)=…

A: Topic = Functions Correct option  = c

Q: Parametric Equations. Show complete solutions. 1. Find the equation of the tangent line (s) to the…

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Q: For the function x-3 f(x) = 2x +5 etermine coordinates of the y-intercept of the inverse function…

A: We can find the coordinate of y-intercept inverse function as below.

Q: 2x e d.x 4e2 – 8e" + 5

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Q: 1 Verify that tan?(csc-1(x)) = x2 – 1

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Q: Find and classify all the critical points of f(x, y) = 2x - 9y - xy + x2 + 5y2 .

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