When using integration by parts to evaluate the integral fx²e-²x dx and du pick u = that du = and v= which means

Q: Solve the following differential equations by separation of variables: y' = ²/² 4tdy= (y² + ty²)dt…

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Q: . Evaluate the for parametric equations x = 3t² - 6t and dx = 3t³ + 3t with respect to the…

A: Given query is to find the Indicated derivative.

Q: Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle…

A: need to find out the critical point.

Q: Find ff f(x, y) dA where f(x, y) = 3x + 1 and R= [0, 3] x [1,3]. R SSR f(x, y) dA =

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Q: Find the Differential Equation whose general solution is y = C₁e4t + C₂e-³t Oy" -y' -12y=0 Oy"-y'…

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Q: 1. dy ax = 3 -2X y-xy³e

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Q: Solve the boundary-value problem y" – 12y' + 36y = 0, y(0) = 8, y(1) = 0. Answer: y(x) = Note: If…

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Q: region

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Q: Find the values of x, y and z that correspond to the critical point of the function ƒ(x, y) = 2x² +…

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Q: The function f(x) = 2x³ − 33x² + 108x - 7 has two critical numbers. X = (enter the values separated…

A: Topic- Application of derivatives We are given, f(x)=2x3-33x2+108x-7we know that critical numbers…

Q: (b) Find the 243rd derivative of f(x) = sin(3x) 3

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Q: (f) Evaluate the derivative. Do not simplify. - (2-7) *** y =

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Q: Determine whether f(x) = = -4x² + 16x - 2 has a minimum or maximum value, and find the value of the…

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Q: 5) Determine the time it takes an amount of money to triple if compounded continuously

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Q: Consider the function f(x): this interval. = on the interval [3, 10]. Find the average or mean slope…

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Q: . (tan¯¹(t),e¯² Evaluate lim (tan-¹(t), e-2t, Inty t→∞

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Q: Determine the least possible degree of the polynomial function shown. The least possible degree…

A: Let's find least possible degree of given polynomial function.

Q: (b) lim (x,y)→(0,0) x² + y² √√x² + y² + 1 − 1

A: Given limit is limx,y→0,0x2+y2x2+y2+1-1 We need to explain why this limit doesn't exist.

Q: H y=x² R

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Q: A current state has a population of 3500. With the rate of 0.23/year, what will be the population…

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Q: e. A manufacturer determines that when x (THOUSAND) units of a particular commodity are produced,…

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Q: If lf Ŕ(t) = et cos tỉ – et sin tj Find the velocity and acceleration vectors.

A: To find the velocity and acceleration vectors for the given position function.

Q: Question Let h(x) = f(x)g(x). If f(x) = x² – 2x − 2 and g(x) = -4x, what is h'(x)? Select the…

A: To find the derivative of the given function.

Q: Find the equation of the tangent line to the function f(x) = 2x² - x at the point where X x = -1.…

A: Given query is to find the equation of the tangent line.

Q: Consider the shape with vertices (1,3),(4,7),(0,10),(-3,5) translate the rectangle so (1,3) lies on…

A: We need to transform the coordinates.

Q: H.W: Salve the following equations.... 一乂 3. H .... Je A zAyf. (X² 3y)...........

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Q: Graph and describe transformation of the following function: f(0) = -3csc (0+)-1 where 0 ≤ 0≤ 2. Use…

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Q: Question 3 Find the transform of the given function by use of a table. f(t) = e4t 1 (A) F(s)= S + 4…

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Q: Basis: Find a basis of the subspace of R³ defined by the equation - 8x₁ +9x₂ - 8x3 = 0.

A: NOTE: Refresh your page if you can't see any equations. . now we need to solve this equation for x1…

Q: I got a Guinness can whose temperature is 21°C. To enjoy it cold at the perfect tem- perature of…

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Q: Determine which of the following differential equations are separable. Do not solve the differential…

A: Separation of variable:- A differential equation satisfy the method of separation of variable if the…

Q: Use differentials to approximate √3.99

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Q: Find the dimensions of a rectangular corral split into 2 pens of the same size producing the…

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Q: A ball is thrown into the air and its position is given by h(t) = - 7.3t² + 73t + 11 where h is the…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

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Q: Question 8 Solve the given differential equation (where the function is subject to the given…

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Q: Use the degree 2 MacLaurin polynomial of f(x) = cos(2x) to approximate cos(2). . (Enter a number for…

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Q: 2. Determine f'(x). (a) f(x)=√√26 (b) f(x) = 26√T (c) f(x) = √26x (d) f(x) = √26.x

A: To find the derivative.

Q: Q= (a) Find the point that is a distance 0.1 from the point P = (5,6) in the direction of v = (1,…

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Q: 2x - 4 Find f ' (x) using the definition of the derivative: f ' (x) = lim h>0 f(x+h)-f(x) / h

A: Given query is to find the derivative using definition.

Q: x 1 3. Bauh. Bd. J... A Xdy. (X² 3y).d.x.=... Jo 2 ....................

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Q: Determine R(t) if R'(t) = <2e2+-4,4 =-1) and R (2) R (2) = <3₁-5,0).

A: To determine R→t if R'→t=2e2t-4, 6t2, 1t-1 and R→2=3, -5, 0.

Q: 1. Let x₁0 for all ne N. (a) If xn0, prove that √x -0. (b) If xn →x, prove that √√√√x.

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Q: Given vectors from the origin r = 3a, + 8a, +a, r=a, -6a, + 5a,, and rc = 7a, - 48,, find: (a) a…

A: The cross product two vectors, say a= a1ax+a2ay+a3az and b = b1ax+b2ay+b3az denoted by a×b is…

Q: • Use partial derivatives to locate critical points for a function of two variables. nd the critical…

A: Here is the solution:

Q: Let Find dy || ¹. y = f(x) = arcsin In 7x. dy dx

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Q: The graph of a function is shown below. Over what interval(s) of x is the function decreasing? V

A: Given query is is to find the interval where function is decreasing.

Q: 2. Evaluate the total derivative of u with respect to x for u = 5x³+y²+z² when y = sinx and z = cosx…

A: Given y=sinx So, dy=cosxdx Given z=cosx So, dz=-sinxdx

Q: Consider the function f(x) = 1 − 6x², − 5 ≤ x ≤ 2. The absolute maximum value is and this occurs at…

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Q: A company that produces cell phones has a cost function of C = 5x² - 155x + 6619, where C is the…

A: Given query is to find the number of units need to be produced to minimise the cost.