Consider the function f(x) = /4-x +1 for the domain (-00, 4]. Find f(x), wheref is the inverse of f. Also state the domain of f* in interval notation.

Q: Differentiate the functions. 3 a) f(x) = 1– 5x + b) f(x) = (x³ + 4)² %3D

A:

Q: u+1 Using u-substitution, the integral Jf(x)dx reduces to a new integral glu) du. If glu) = , evalua...

A: Given  g(u) = u+1u and  ∫f(x) dx = x + lnx-1 + C

Q: Use Green's Theorem to calculate (4z? - 3yz)dr + (3zy + Vy? + 6)dy, where Cis the circle (r – 1)2 + ...

A: Greens theorem

Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values ...

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. d.x +C Væe(20...

A:

Q: Calculate y°dz – yz²dy – sen(2)dz, where C'is the path connecting the point A(-2, 2, 4) to the point...

A: We will calculate the integral ∫Cy2dx-yz2dy-sinzdzwhere path starts from point A-2,2,4 to the point ...

Q: 1. What is (3x) ? 2. What is (x*+ x)? 3. What is (2-32)? 4. What is (6v - 3v + Sv)? 5. What is (x-1)...

A: As per the guidelines we can solve 3 parts only 

Q: Situation 1: Find the area bounded by the curve x^2 = y + 2 and the line x + y = 0 1. Using Simpson'...

A:   A=∫-21 (-x-x2+2) dxA=[2x-x22-x33]-21 A=2(1+2)-12+2-13-83 A=112 A=5.5 square units

Q: Suppose f(x) = "6r V1+f dt.

A: Topic = Integration

Q: tan x 2. (a) lim e →号一 (b) lim sin (tanh 3x) エ→十0

A: limx→π2-etanx

Q: 4x2 + 4y? + 122 = 9 and the point P = (1, 1, 1) on this surface. A. Starting with the equation x =1+...

A: We have to find the normal line through P and tangent plane through P.

Q: The cost, C (in $), to rent a car for n days from the EZ4U rental company is given by the linear fun...

A: see below the answer and explanation

Q: 8-2x (f) lim- X-4 x -x-12 Vx² +16 –4 lim- (g) x' +8 lim x-2 x+2 (h)

A:

Q: 2. Divide the class into groups of 10. Measure the height of each member. Find the sampling distribu...

A:

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

A:

Q: Directions: Determine whether the given function is a. continuous or not b. differentiable or not. A...

A:

Q: the weight of an object to its volume. re Density.

A:

Q: Find the distance between the points (distance formula) 1.(3, 2), (4, -3) 2.(-5, 1), (-7, -3) 3.(-1,...

A: Distance between two points (x1,y1) and (x2,y2) is (x2-x1)2+(y2-y1)2. Note : As per our Guidelines ...

Q: topic: calculus of polar curves 1. Find the slope of the curve r = 2cos 4Ɵ 2. Find the slope of th...

A:

Q: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h f(x...

A:

Q: The curve C with equation y = f(x) passes through the point (1, -3). Given the following, find f(x) ...

A: We know, ∫xndx= x(n+1)/(n+1)

Q: An observer is standing in a lighthouse 96 feet above the level of the water. The angle of depressio...

A: An observer standing at a height of 96ft on a light house  The angle of depression of the buoy is 22...

Q: 6. Consider -dx. Transforming the integrand, the result will be k , where k is a constant. What is u...

A:

Q: • f(x) (x) , evalu:

A:

Q: Compute the LU factorization of the following matrix. No row interchanges will be necessary. You can...

A:

Q: 1. Consider the function f(x) whose graph is given below. If a discontiuity is Emumerate all discont...

A: Discontinuity

Q: Compute P,(f,0)(x) for the following function: f(0) = 42, f"(0) = 23, f) (0) =19, f®)(0) = 17, f("(0...

A:

Q: 30 3 120 x f(x) = 2x-3 X + 1 n = 4 3 Pa(x) = 3 1+ x -x+x -3+ 5z- 522 +5-54 | Solution or Explanation...

A:

Q: /4x+ – 12x² +7 xdx . Evaluate the integral A) -(4x4 – 12r²+7)/2 +c 24 © ! (21--3)/- 121+7 – 2 m 21--...

A:

Q: Use synthetic division to determine whether x - c is a factor of the given polynomial. x3 - 11x2 + 3...

A: By using the synthetic division to determine we have to check whether x-c is a factor of the given p...

Q: Then find the length of the indicated portion of the curve. r​(t)=3e^t cost I+(3e^t sin t) j−3e^t k​...

A:

Q: 5. Find the limit of lim x* +0-x

A: Topic = Limits

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) : 1 n = 4, C = 2 Pa(x) =

A:

Q: Using Figure 1, complete the following function. Figure 1 tane = %3D O v/r u/r O r/u O r/v O vlu u/v

A:

Q: dr if r =Vs+1 and s=161-20t . dt 1. Find -

A:

Q: cot (2x) dx . V cot2(2x) – 15 Evaluate the integral csc (2x) -Arcsec 4 A +C 4 O - - In [cor (2r) + V...

A: This question can be solved using the concept of integration by substitution and some special integr...

Q: 3) For f(x)= cos(20x), use Taylor polynomials to estimate f(1/40) to within 1/100. Do not forget to ...

A:

Q: Find the distance between the points (distance formula) 5.(2a+c, 2d), (2b-c, 2c) 1.(3, 2), (4, -3)

A:

Q: dy de + 2xy = 2xe-x².

A:

Q: Find the derivative of the function. h(t) = (t + 5)2/3(2t² – 1)3 2( 22 – 1)2[202² + 90t – 1] h'(t) =...

A: In your solution please replace x to t

Q: Using Figure 1, complete the following function. (-8, - 6) Figure 2 csce = 5/3 5/4 -5/3 -5/4

A:

Q: Given the taylor series at 0 for 1/(1-x2)= 1+x2+x4+x6+x8+...+x2n Use above to find the taylor serie...

A:

Q: fIntegrate the functon. fexng) the functrom. fixng). aver.the... 2. 1 -xーye 2. reginm.(.disk.). Does...

A: The solution is given in the next steps.

Q: Vx+11-4 (b) lim- x- 5 X-5

A:

Q: Differentiate the functions by using product or quotient rule. a) f(x) = (1 – 3x?)• e Зx+1 b) f(x) 2...

A:

Q: Evaluate lim (r+ 2) cot(²+5x+ 6). 2+-2+

A:

Q: a2/2 if l띠 3. Find vertical asymptotes, if any, for y = f(x). Find oblique asymptotes, if any, for ...

A:

Q: Find the derivative of the function. y = cos V sin(tan(3x)) )

A: Topic = Derivative

Q: Question 15 Evaluate the integral V4x 4x4 12x2 +7 xdx. (4x* – 12r?+7) /2 +C 24 B(2x-3)/4x4- 12x2+7 +...

A:

Q: Prove that the following statement is true for all positive integers. 1 1 1 + + 4 8 1 2" – 1 + 2n Pn...

A: Given; Pn : 1/2 + 1/4 +1/8 +...+1/2n =(2n -1)/2n