2. Find the derivative for each of the following, be sure to use proper notation and simplify when needed (both, positive or negative exponents are permitted. 1 b. y = 4t5 (3) m = V6n a. (3) (3) c. v = (4t3 – 6t)5 %3D

Q: dx X Jioin? x-9

A: ∫1x16ln2x-9dx

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A:

Q: Given the following trigonometric values, find the angles ? within the interval 0 ≤ ? ≤ 2? that sati...

A:

Q: Use partial fractions to find the indefinite integral. 9 – x2 dx 5x3 5x + X

A:

Q: For the sequence {an}, with lim an = 9, this means the terms in the sequence approach 9 as n becomes...

A:

Q: Question 15 Find the distance from S= (1,1,5) to the line L: x=1-t, y=2-1, z=31.

A:

Q: Solve the differential equation by integrating factor method, dy (x + 1)2+ (x +2)y = 2xe¬*. dx

A: Given,            x+1dydx+x+2y=2xe-x.To find : Solve the differential equation by integrating factor...

Q: 10 (x. What is the appropriate formula? Given: @ 3 fa"du 2 B) Sa" du © Sa"du D

A:

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A: We will do second derivative test to find minimum area.

Q: cos 2X 80 dx csc (x) sec (X) CSC

A:

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

A:

Q: df Q4) A) Find dx by using chain rule if f = , u=-1 , x=-1 u+1 B) Evaluate the following integral: S...

A: A) To find the derivative of the given function f=u-1u+12 with u=1x2-1

Q: S sin?3ß cos11ßdß

A: ∫sin23βcos11βdβ ∫ (1-cos6β)(cos11β)dβ/2 ∫(cos11β)dβ/2 - (cos6β)(cos11β)dβ/2 (sin11β)/22 - ∫(cos17β +...

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral: SV2...

A: This question is based on chain rule differentiation and indefinite integral.

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: From definition of Taylor series about center c of a function f(x) we know, f(x)= ∑k=0∞fk(c)xkk!

Q: Given the following graph, what is the exponential equation that relates the variables?

A: Here x = independent variable y = dependent variable k = y - intercept = ( 4.5 0.1) m/s2

Q: ( sin23ß cos11ßdß

A: solve integration  2sinA.cosA=sin2A 2sinAsinB=cos(A-B)-cos(A+B)

Q: Integrate the following: xdx 1. S x²-x+1 xdx 2. S V9x4-1 dx 3. S XVx-1

A:

Q: 12x Ja +9)6 dx

A:

Q: III. Answer the following questions. 1. A window in the shape of a rectangle surmounted by a right t...

A:

Q: Q5) A) Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x ( then find the area o...

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 5 cosh(/x) xp

A: ∫5cosh(x)xdxlet x=tdifferentiate on both sides12xdx=dtThen ∫5cosh(x)xdx=5∫2cosh(t)dt

Q: raluate the integral / V4x4 – 12r2 +7 xdx. A - (4x* – 12r? +7)½ + c 24 B - {(2r²– 3) /4x+– 12x²+7 – ...

A:

Q: SxV16ln? x – 9 1 dx xV16ln? x – 9

A: We put logx=u/4 and differentiate both sides with respect to u and solve it. Follow 2nd step.

Q: Solve the given initial-value problem. The DE is a Bernoulli equation. y1/2 dy + y3/2 = 1, y(0) = 16...

A:

Q: Look for the volume of the solid generated by the Solid of Revolution revolving region bounded by th...

A: Let's find. 

Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1+x 1 F(x) = 1 +x+ :·...

A: Using the binomial series expansion: (1+x)k=1+kx+k(k-1)2!x2+k(k-1)(k-2)3!x3+...                     ...

Q: 2. Find the derivative for each of the following, be sure to use proper notation and simplify when n...

A: As per guidelines I can only solve first three subparts , remaining can be reposted

Q: Question * Using integration by parts and taking a > 0, the integral S, x In(ax)dx is equal to:

A:

Q: Practice: Find the volume of the solids generated by rotating the area bounded with the given functi...

A: Question - a Given functions, x=y2x=2-y2 Axis of rotation, y=1 Formulas used: ∫xndx=xn+1n+1

Q: Verify the inverse function theorem of the function y = 4x2 +4x + 9.

A: Solution is given below:

Q: Use the function f and the given real number a to find (f1)(a). (Hint: See Example 5. If an answer d...

A:

Q: Answer and give a brief (1-2 sentence) explanation for each of the following questions. (a) Suppose ...

A:

Q: Question 1: Differentiate the functions. a) f(x) = 2 – 5cosx +x4 + 3* b) f(«) = +

A: I am attaching image so that you understand each and every step.

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)5 1 f(x) : (1+x...

A:

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A:

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A:

Q: (-1)"3nx" n2 – 5 Determine the interval of convergence of n=1

A:

Q: Consider the series E ne-n? n=1 If we let f (x) = xe = re-r2 then S f(x) dx %3D O is finite. O is no...

A: The given series,     ∑n=1∞n e-n2

Q: Use the formula for the binomial series: m(m-1).(m-k+1). k! m(m-1) (1+ x)" 1 + mx + 22 + ... + %3D 2...

A: We have to obtain the Maclaurin series for 1+x5

Q: 12. Simplify the following rational expression for the function f (x) = 5x2 f(x + h) – f(x) h

A: Given f(x)= 5x² So, f(x+h)= 5(x+h)²=5x²+10xh+5h²  

Q: By completing the square, dx the integral S is equal to: (x+5)Vx²+10x+21

A:

Q: (a.) the critical numbers of f (b.) all relative extrema of f (c.) the intervals on which f is incre...

A:

Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2 ...

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: Q.2\Prove the Maclaurin series: In(1+ x) = En=1' (-1)"-1x" ,-1<x< 1 . %3D

A: f(x) = ln(1+x)f0(0) = 0f1(x) =f'(x) =11+xf1(0) =1f2(x) =f''(x) =-1(1+x)2f2(0) =-1f3(x) =f'''(x) =2(1...

Q: Using appropriate substitution and taking a + 0, 3tan(ax) the integral S dx is equal to: cos² (ax)

A:

Q: Use the formula for the binomial series: (1 + x)" 1 + mx + m(m-1)2 m(m-1)..(m-k+1), + + ... ... 2! k...

A:

Q: Given: Sum of the points of the ellipse from foci = 30 Foci: (2,1) (10,1) c = 4 a=? b=? Center: ...

A:

Q: hdefinite integral using integration by parts with the given choices of u and dv. X COs 8x dx u= x, ...

A: We will fill in the blanks with appropriate values. 

Q: Identify the problem whether a Permutation or Combination. Write the given of the problem and solve ...

A: Permutations and combinations