Differentiate y = 21/2 4 - x (4 – x³)'"2 -

Q: me limit below represents a derivative f'(a) Find f(r) and a lim h-0 (5 + h)² – 25 h. 10

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Q: Find the Taylor series generated by fat x = a. 3 f(x) = a = 1

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Q: A projectile is shot upward from the top of a 220-foot building with an initial velocity of -22 feet...

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Q: 6. Find a set of parametric equations for the line tangent to the space curve at the given point. 2 ...

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Q: Determine whether the integral is convergent or divergent. The integral from negative infinity to 0,...

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Q: A particular country's exports of goods are increasing exponentially. The value of the exports, t ye...

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Q: 15 What is the exact value of tan (sinr) where r = 17? Provide your answer below:

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Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

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Q: Find the Taylor series generated by f at x= a. f(x) = 2*, a = 1 Choose the correct answer below. O A...

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Q: Find the differential of each function. (a) y = etan(nt) dy = (b) y = V4 + In(z) dy =

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Q: Find the Taylor polynomial of orders 0, 1, 2, and 3 generated by f at a. 5x f(x) = cos x, a = 6 Po(x...

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Q: Consider the function f(x)=1/x on the interval x>=1. find the Surface area and volume of the solid f...

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Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: 3. Find the dimensions of a open topped box that maximizes the volume with the constraint that the s...

A: We need to find dimension of an open box that maximizes the volume.

Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: Find the derivative of the function. y = a6 + cos6 x y'(x) =

A: Given

Q: Evaluate the following expression. arccsc(/2) Provide your answer below: Radians

A: We can find the answer as below.

Q: Find the distance from the point (3, 3, 5) to the plane 3x - 3y + 3z = 5. Leave your answer correct ...

A: topic- distance of a point from a plane 

Q: 137 What is the value of cos-(cos d) where d = 15T radians? If undefined, enter Ø. 2 Provide your an...

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Q: Show that V is a subspace of R³: V is the set of all (x, y, z) such that z = 2x + 3y

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Q: lenry made juice from a recipe that called for 1 cup of sugar, 3 cups of lime-drink mix, and 2 gallo...

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Q: Find the maximum rate of change of f(x, y) = In(x² + y?) at the point (-4, -3) and the direction in ...

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Q: Find the distance between (1, 2, 3) and (-1, 3, 4)

A: Consider the points  1,2,3  and   -1,3,4  

Q: To the nearest tenth, what is f′(k) if f(x)=0.09e^xln(x) and k=8?

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Q: Find a simplified form of the difference quotient for the function. 8 f(x) = x2

A: We have to find simplify form

Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a ...

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: Find the length of the parabola given by c(t) = (t, 1) for 0 < 1 < 5. Hint: Use the formula / VI+i' ...

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Q: Question Select your answer. 1, T - 1, if a > 0 if z < 0 Given f(x) = , estimate lim f(x). does not ...

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Q: Find the Taylor series generated by fat x = a. f(x) = 9*, a = 3 Choose the correct answer below. 729...

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Q: Consider the following function. +] - 2x + 2 3 2 (a) Find y'-f"(x). "(x) = (b) Find the critical val...

A: Topic = Derivative As per guidelines , At  a time only three sub-parts can be answered.

Q: The graph of fis given. State the numbers at which f is not differentiable. (Enter your answers as a...

A: If there is a sharp point at x=a on the graph , then function is not differentiable at x=a. If funct...

Q: The tangent line to the graph of y=f(x)at the point (1,11) has the equation y=3x+8 (a) Find f′(1) ...

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Q: Calculate the improper integral if it converges, or show that it diverges. 3x4 dx 5 – 1 -

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Q: Show that the equation has exactly one real root. 3x + cos(x) = 0

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Q: Differentiate. y = In (8x? -7x+8) y':

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Q: Use implicit differentiation to find y' for the equation below and then evaluate y' at the indicated...

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Q: Use implicit differentiation to find y' and then evaluate y' at (3,0). 9 eY =x2 -y? %3D y' =] y'l(3....

A: topic - implicit differentiation

Q: Test the series for convergence or divergence. 3"n! 13 · 18 · 23 ... (5n + 8) n=1 Use the Select v a...

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Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),...

A: We have to find dsdtt0=π4

Q: 1. Find an equation of the line that is tangent to the graph of f and parallel to the given line. 1 ...

A: Topic = Functions

Q: (a) Find the differential dy. y = ex/4 dy = (b) Evaluate dy for the given values of x and dx. x = 0,...

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Q: Find a simplified form of the difference quotient for the function. f(x) = /x- 8

A: Difference quotient for function f(x)=x-8

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series c...

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Q: 2. Sketch the graph of f' given the graph of f. Explain how you found the answer. y 10- 9- 5- -10-9-...

A: The objective is to sketch the graph of f'.

Q: 1. Find the values of x,4 and z that corvespond to the critical point of the funchion Z="f(x,4)= Sx?...

A: We have to find critical points of f(x,y).

Q: A) What is the point of intersection between the plane x – 2 y +3 z +1 = 0 and the line r = + t? B)...

A: Use substitution method

Q: ind all critical points of the function f(x) 4x2 %3D 5x2-2x+4 Jse symbolic notation and fractions wh...

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Q: The graph of f is given. State the numbers at which f is not differentiable. y -4 -2

A: In this question we have to state the number at which f is not differentiable according to the given...

Q: Use implicit differentiation to find and for x? + 2y2 + 3z2 = 1. əx ду

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Q: Find the exact anser for t and leave the answer with the logarithm in the answer. 40e−0.2t = 12

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