Instructions: Use Rules of Differentiation to differentiate the following functions. Show your solution and simplify your final answer. 4x³+2x? 5. y = 3x*+5 6. f(r) = (r² + 2r – 3)(3r + 4) 3. y = e* sec x

Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about * = x0 and then find the nth Taylor...

A: Let's find. 

Q: -8 Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....

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Q: csc x du (3T 5. If u = f(x), then dx sin x – cos x Compute f и %3D (a) 1 (b) -1 (c) 0 (d) 2

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Q: 5. Solve a) In(x+1) = 3 b) e2 – e = 2.

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Q: Vx-3-V9-x 3. lim X-6

A: Solving the problem by finding the limit of th3 function.

Q: 1+ In x tan(f(x)) Find f(x) so that when u = f(x) the integral | dx can be rewritten as cot u du . А...

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Q: 2022" + n 2022 (d) lim sin 2022! + n!

A: We have to find: limn→∞sin2022n+n20222022!+n!. We can take the limit inside of sin as the limit is o...

Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

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Q: Csc X Given: dx Vcor?(글씨)-4cor(글씨)+4 -x)+4 Find: u ct 1 cot2 1 x) - 4cotx) +4 cot cor()- acot( X+ 4

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Q: -In 3 e* In 2 V4 - e*

A: As per our guidelines we are supposed to answer only one question i.e. the first question. For the s...

Q: Use sigma notation to write the Taylor series about x = xo for the function. e; xo = 10 O 00 e10 E* ...

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Q: 11. The integral of an(In|4x-12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. 2 С. 4 D.

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Q: Create a bucket by rotating around the y axis the curve y = 3 ln(r- 1) from y = 0 to y 10. If this b...

A: Given: Create a bucket by rotating around the y-axis the given curve, y=3lnx-1 from y=0 to y=10 Dens...

Q: f (1,0) Based on the figure above, (f-1)'(0)

A: The figure given is   

Q: One of the following is an improper integral. - In 3 e* dx JIn 2 V4 – ex dx xV16 – In x - dx · In 2 ...

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Q: One of the following is an improper integral. - In 3 e* dx 4 – ex dx In 2 xV16 – In x dx cln 2 dx x ...

A: In this question we have to find the value of Improper Integral. Note: As per our policy we are supp...

Q: z° – 6z' + 4z – 2 dz |

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Q: 15-16 Find the number e that satisfies the conclusion of the Mean Value Theorem on the given interva...

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Q: 1 dx Evaluate -1 x2 O 2 O -2 O O

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Q: The volume, V, of a sphere in terms of its radius, r, is given by V (r) = Tr³. Express r as a functi...

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Q: Find the derivative of the function f(x)=2x−73x−2 at x=2

A: topic - derivative of a function

Q: Enter the value of L- 1.27].

A: Floor value of x  is given as the greatest integer that is less than or equal to x

Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in ...

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Q: 6. The number x, 2x + 7, 10x - 7 forms a Geometric Progression. Find the value of x A. 5 B. 6 C. ...

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Q: Given: S 2x (3-5x+)'dx Find: Formula O -2 Ju'du 0 2 fu'du o fưdu Jư du 10

A: Given problem:-

Q: Evaluate the integral V4x4 – 12x2 +7 xdx

A: Using integration of square root of x2 - a2 and follow step 2nd . 

Q: The Pauli Exclusion Principle tells us that no two electrons in an atom can have the same four quant...

A: Please see the below picture for solution. 

Q: 7Q b) TR = (Q+3)

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Q: 2. Let dx be given . If u = e* + 1, then the resulting integral is f(u) du. Compute f(3).

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Q: Evaluate :// F. d5 , where F = and S is the helicoid with vector equation r(u, v) upward orientatio...

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Q: u du Form Answer 5sinx dx Ex. J a+ 2cOsx 3+ 2cosx -2sinxdx uż du -5V3 + 2cosx + C 3 15. Given: •dx 5...

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Q: 22. Determine f(x) so that cos(In²x) f(x) dx = sin(In²x) + C (a) 2 In x 2 In x (b) Inx (e) NIK

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Q: Evaluate the integral tan 4x S- Vtan? 4x – 24 In/tan 4x + /tan² 4x – 24| +C O 1 sec 4x +C Arcsec 5 O...

A:     14lntan4x+tan24x-24+C' =14lntan4x+tan24x-24' +C' =sec24xtan24x-24+0=sec24xtan24x-24 So, the firs...

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, Y...

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Q: If inflation grows continuously at a rate of 6% per year, how long will it take for $8 to lose half ...

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Q: || x? zdS, where S is the part of the plane z = 1 + 4x + 3y above the S. Evaluate rectangle [0, 3] x...

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Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show ...

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Q: Graph the function f(x)=−4x2f(x)=-4x2 and draw the tangent lines to the graph at points whose x-coor...

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Q: Find an equation of the tangent line to the graph of the function at a given point. Note: You may/ma...

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Q: 11. The integral of nunex dx is bln]sec(In(2x)")|. What is b? A. 2 B. 2 C. 4 D.

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Q: dx Evaluate * (1-2x)² (1–2x)² O 1 1 2 O-1 o 1 2

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Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for ...

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Q: Question 2: Illustrated below are two tangent lines drawn at 2 different points on the curve whose f...

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Q: Identify all three (distinct) solutions to the equation z3 = 27i. Write your answer in x + iy form.

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Q: For the integral which of the following options is corn A. lim (x- 1)|+ lim (x – 1)3 B. lim 3(x – 1)...

A: Find your answer below 

Q: dx Given: 2x- 3xlnx Find: du dx 3 dx dx 3 dx ---

A: Explained below 

Q: 2 f(x)dx Given: There is a function F(x) such that when u= -x³, the 2 du resulting integral is Evalu...

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Q: 18. dx The integral - can be rewritten as V1 - x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī -s) s--00 s--00...

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Q: dP Recall that in a class this week, we discussed a problem where we are given = rP. K К -Р where r ...

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Q: 3-Vz dz 2+yz

A: Power substitution  is a  method of integration that aims to replace the nth roots in a function, wh...