lim x→0 lim x→0 e. lim csc x-cotx sin x 1-cos.x 2.x² COS X 4x

Q: Let r(t) = (²,1-1,4t). Calculate the derivative of r(t) a(t) at t = 5 assuming that a(5) = (5,-8,6)…

A: Given that .We have to calculate the derivative of  at .

Q: Calculate the derivativer(g(t)) using the Chain Rule. r(t) = (e¹, e¹¹,9) g(t) = 4t + 4

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Q: Many populations are facing negative growth rates. If the population of the Ukraine was 60 million…

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Q: dy dx - x7e² = 2e", y(0) = 1

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Q: (c) Hence compute x6(log x)5 dx.

A: From part a we have results

Q: What is the unit vector with the same direction as the vector v = 3i − 9j?

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Q: The pH of a solution is given by the formula pH = log 10- in which H+ is the concentration of…

A: The pH of a solution is given by formulaWhere,  is the concentration of the hydrogen ions in gram…

Q: 2. -y (y+₁)-√y+₁ dy

A: The given integral is We can easily solve this problem using the substitution method.

Q: By analysing the normals, determine if the three planes intersect in a point. T₁: X-5y + 2z-10 = 0…

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Q: Find all the second-order partial derivatives of the following function. h(x,y) = 4xe + 7y +5

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Q: Evaluate the limit. 1², -5t, 7 ) = (xo, Yo, zo) (Use symbolic notation and fractions where needed.)…

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Q: Given f(x, y) = 10√/8x5 + 7y + 2xy, find fz(x, y) = fy(x, y) =

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Q: Determine the equation for the tangent to the curve f(x)=In(1+e') when the tangent is parallel to…

A: Here, we need to determine the equation for the tangent to the curve f(x) = ln(1+e^x) when the…

Q: Sue's grade in her math class is related to the number of hours she studies. The rate of change of…

A: here we have to find the score of the sue if she studied 20 hours.

Q: Find all the second-order partial derivatives of the following function. w=xsin (6x²y)

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Q: If x² + y² = 4, then O false O true dy dx ==3 Y

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Q: / X 9 - x² dx

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Q: Prove one of the following formulas from the table of integrals: S: √a²-x²2 a²x + C dx x²√a²-x²

A: Note :-Since you asked multiple questions , according to our policy we can solve only first question…

Q: Find the solution of the differential equation r' (t) = 5r(t) with the initial condition r(0) = (2,…

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Q: Find the particular solution to the following differential equation using the method of variation of…

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Q: 5π Determine the exact value of sin- 12

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Q: Let r(t) = (tª, t5) g(t) = sin(3t) Evaluate the derivative using the Chain Rule. (Use symbolic…

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Q: Problem.4. Sketch a graph for f(x) so that the following properties are true: lim f(x) = 5 Property…

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Q: 1. Perform the indicated operation. X (1-2x)3 dx

A: We need to evaluate the following integral

Q: Suppose that f(x) = 19x² - 8x. (a) F'(x) = (b) The slope of the graph of f(x) at x = 5 is (c) The…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Which of the following graphs is consistent with the differential equation dx = x y

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Q: Question 10 Given that sine and Show you work 2 0<0 < ¹ PENCIL THIN 2, what is the exact value of…

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Q: A $4536 loan was repaid with $5978. If interest was 4.8% compounded semi-annually, for how many…

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Q: Compute the derivative (r₁(1) r₂(t)) if r₁(t) = (15,1³,16) r₂(t) = (e²¹, est, e7¹ ) (Use symbolic…

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Q: Apply the midpoint and trapezoid rule to the following integral. Calculate the approximations and…

A: Let's solve the integral using midpoint method.So we divide interval [1,5] into 8 subinterval of…

Q: For the function f(x,y) = 6 of find and 8x+3y' dx dy

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Q: For the function f(x,y) = In (7x+2y), find and əx dy

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Q: 6. Twenty mathematics textbooks must be stacked in a row on a shelf. There are 5 identical calculus…

A: This is question of permutation and combination.Here we have to use of both Further calculation is…

Q: a square represented by the graph as follows. Find the fourier transform pair.

A: The Fourier Series is given by :Here, 1. f(x) is the function2. L is half of the period of the…

Q: (13) Sup (14) The coefficient of x3 in the Maclaurin series expansion of e2x is: A) - B) C)- D) is…

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Q: Solve the following system of equations.

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Q: Using separation of variables, solve the initial value problem, dy dx y = In -8e ex8+16xe +8 - xe =…

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Q: 4. Without graphing, complete the following for the function k(x) = 2 (5*). (a) Describe the shape…

A: Without graphing, to complete the following for the function .(a) To describe the shape of the graph…

Q: If an object is moving with v(t) = 3 cos(t) and the position X(0) = 1, what is the position of the…

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Q: Parametrize the intersection of the surfaces y² - z² = x - 6, y2 + z² = 25 using trigonometric…

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Q: Describe all of the transformations applied to the parent function f(x) = x² to sketch g(x) = 5(x +…

A: We have,   f(x) = x2    g(x) = 5(x+3)2 - 2

Q: Q6. The population of foxes in a provincial park is modeled by the equation P(t)= +40, where t is…

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Q: A mass of 4 kg is attached to a spring with a spring constant of 128 N/m. The mass-spring system is…

A: Here we have work out the damped harmonic oscillator's equation of motion in order to determine the…

Q: The following table gives some of the values of g(x), g'(x), f(x) and f'(x): Use the table to find…

A: Question 1)We first need to find the derivative then apply the values from table:-Now, we find the…

Q: Maximum/minimum point(s) for y=sin2x-cosx-4x on interval 0<x<2π. The value(s) should be in radians.…

A: We are given the following information.We will find the maximum/minimum points for y=sin2x-cosx-4x…

Q: F. ds, where S is the entire surface of the solid half ball x² + y² + z² ≤ 1, z ≥ 0, and Calculate…

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Q: Find the solution to the initial-value problem dy dx 4x = y²e¹* sin(2x), y(0) = 1

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Q: What is the general solution to √æ² +3¹² = 2x ? dz Oy= 2√²+3+C Oy=√√√²+3+C Oy=C√√√x² +3 Oy= 2√x²+3+C

A: given

Q: Minimize Szy +25zz + 5yz subject to zyz = 1 with z>0, y> 0, z > 0.

A: We need to Minimize S = xy + 25xz +5yz subject to xyz = 1 with x&gt;0, y&gt;0, z&gt;0.

Q: What is the smallest value of the number n so that the graph of the following function have a…

A: f(x)= (-2x4+1)/(6xn-3x2-1)We have to find smallest value of n for f(x) has horizontal asymptotes