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Q: Find the equation of the tangent plane to at the point (0, 5, 34). z = z = e² + y + y² +3

A: The given equation is; z=ex+y+y2+3 Point (0,5,34).

Q: a) b) (2,5,-1). Find the values of a,b in a +ib=(3+i)(2-3i where i=√√-1 Find the position vector…

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Q: Find the solution of the given initial value problem. ydx + x(ln x - ln y - 1)dy = 0 y(1) = e.

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Q: Use a calculator to solve the following equation for on the interval (0, π). cot (0) =1/2

A: cot(θ)=12tan(θ)=1cot(θ)=2tan(θ)=2θ=tan-12θ=63.4349

Q: Evaluate the limit: lim+∞ In √x+5x 7x

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Q: Convert to a logarithmic equation. Gf=A

A: lnxn=nlnxlnab=lna-lnbgiven  Gf=A

Q: 4. A parabola has focus F( 11, 8) and directrix x= -17. Find its standard equation

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Q: Consider the function f(x) below. At what value(s) of x are the inflection points? Enter answer…

A: for inflrction points  put   f''(x)=0d dx(xn)=nxn-1d dx(constant)=0

Q: Given the following graph a. Evaluate f (3). f(3) = Number b. Solve for f(x) = 3. n ril H Submit…

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Q: Suppose that f(x, y, z) = x²yz - xyz³ is a function of three variables. 1. Find the gradient of f(x,…

A: The given function is; f(x,y,z)=x2yz-xyz3.

Q: Identify which of the following formulas applies to the future value of a series of payments, with…

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Q: Evaluate the integral below taking as the region bounded by y = x and y = x². ]] (3x (3x + 1)dxdy

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Q: Suppose that you have open a saving account with initial deposit of $ 5000, you continue to deposit…

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Q: What is the size of the payments that must be deposited at the beginning of each 6-month period in…

A: Given query is to find the semiannual payment.

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Concept: Trapezoidal rule : ∫ydx= h2[y0+y6+2(y1+y2+y3+y4+y5)] Simpsons one-third rule: ∫ydx=…

Q: • [ε (a) Evaluate S (b) Evaluate 3.re dr. r² sin z dr.

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Q: what is math

A: Definition of mathematics

Q: The area of the rectangular piece of cardboard shown below is 198 square inches. The cardboard is…

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Q: Find the requested value (to the nearest dollar) and tell what each of the other values represents.…

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Q: Find lim (1+ I-X 4 T

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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

Q: 5. Find the equation of a parabola with vertex at the origin whose properties are given below. a.…

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Q: (b) (-2)-1 7" n=1

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Q: The function f(x) = 2x³ - 45x² + 300x + 9 has one local minimum and one local maximum. Use a graph…

A: Topic - Local extrema's of a function We are given an equation, f(x)=2x3-45x2+300x+9And it's known…

Q: A bacterial culture grows according to the formula P = Poat. If it takes 9 days for the culture to…

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Q: Evaluate f(x) = 3 sin x + 5 cos at x = π/3. 1. f(π/3) = 4 4√3 2. f(π/3) 3. f(π/3) 3√3 4. f(π/3) =…

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Q: A cadet engineer determines that when x hundreds units of a particular commodity are produced, the…

A: Topic- Application of derivatives We are given that A cadget engineer determines that when x…

Q: 4 A stone is thrown upwards out of a window, and the rate of change of its height (1 metres) is…

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Q: New question: 37 please as well

A: The given function is; y=xx.

Q: Directions: Show all your work neatly and in order. 1. Find the mass of the solid E bounded by the…

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Q: 8 2 √√√8x - x² dx 0

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Q: 1.1. Evaluate the following integrals: a. ²x dx b. (2x+3)√2x-1 dx

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Q: Evaluate the limit: lim, +∞ (e² + x) =

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Q: 2y dx (1-y)' 7

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Q: Find the derivative (be sure to simplify): f(x) = sinh(ln(x²))

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

Q: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e-0.21x,…

A: Given P = 14.7e-0.21xwhere P = atmospheric pressure in pouds per square inch x = number of miles…

Q: Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find…

A: WE can determine if each of the following vector field is the gradient of a function f(x,y) .

Q: Consider J₁ x²y dA, where R is the region bounded by 0 ≤ x ≤ 2, x ≤ y ≤x+4. R

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Q: 15 4 12 x

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Q: Use the linear approximation of f(x, y) = e²x²+2y at (0, 0)

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Q: a) Sketch by hand a slope field for the differential equation y'= x/y. Use it to sketch the four…

A: We need to find slope field.

Q: Find the derivative (simplify, but do not rationalize): f(x) = sinh ¹(x³)

A: Given: f(x) = sinh-114x3

Q: (c) Check that your solutions t substituting the expression 63. xy + 2x + 3x² = 4

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Q: SHOW COMPLETE SOLUTION Find the points of intersection between the circle (x-2)²+(y-6)² = 40 and…

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Q: Problem 2 Consider the function f(x) = x³ 4x² +10. Find the x- coordinates of the local extrema.…

A: We have given function  fx=x3-4x2+10 Derivative of the function is given as  f'x=ddxfx…

Q: = SCADX (40x e**²-5) dx 1. S[(GN=51) 10 Jax = log2 (OXP²41) 6X 7- ² 105_ [ [10CC (1014 4X²-5 8. 5 e…

A: Note:  As per our guidelines we are restricted to solve more than 3 subparts of a problem.…

Q: An object is projected directly upward from the ground with an initial velocity of 128feet per…

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Q: Solve: dy/dx = −(y − 27) ^2/3 , with y(0) = 91. Express your answer as y=f(x).

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Q: (b) Where is the function f(x) = x¹e* a maximum?

A: Let's find maximum value of function and at which value of x.

Q: Prove or give a counterexample: Given x > 0. If x is irrational, then √x is irrational.

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