- courses / MATH1200 / Current Activity / Worksheet 1 From the following results, determine whether the function f(x) = (2x + 4, z<4 8, x = 4 %3D is -x + 16 z > 4 continuous at x = 4. Justify the conclusion. (i) f(4)= (ii) lim f(x)= (iii) lim f(x)= 24+ (iv) Justification AnswerD

Q: 1. Evaluate the derivative of f (x) = Vx? – 1, using the following formula. f(x+h)-f(x) a. lim h b. ...

A:

Q: d Compute [(2r* + 5)(4x–1] at x=} 2 24 Your answer

A:

Q: 15-20 1 Solve the initial-value problem. 15. x²y' + 2xy = In x, y(1) = 2

A:

Q: The graph shown below is fx) = -(x - 1)2 + 5. What is the integral function g(x) that defines the ar...

A:

Q: Given f (x)=sec.r-/2 tan .x , find f'(:).

A:

Q: -1 For f dx

A:

Q: Given that y, (x) = x-1 and y, (x) = x3/2 are solutions of the differential equation 2x2y" + xy'-3y ...

A:

Q: Question 5 x3+5 Determine f '(x). f (x) = (A 1- 10x-3 B 3x2 3 2 (D 5x4 + 10x 2.

A: Given: fx=x3+52   As we know that; The sum./difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1 A...

Q: Consider the function fix) sin x. Complete the table below and sketch its graph. x011/6 11/2 5n/6 n7...

A:

Q: (C) Desoibe the relationship between the graphs. The graphs of fand are reflections of cach other ac...

A: solution:-f(x)=x3/7(a)y=f(x)=x3/7x=y7/3hence,f-1(x)=x7/3 (b) Graph

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A:

Q: Trace the curve of the following equations by giving the a. Intercepts done b. Symmetry done c. Vert...

A: Equation of a curve is giveny2=2x4-5x3+3x2+4x-20x2-3x+2

Q: 12. y = x2 – 2x + 3, x – axis, x = -2, x = 1 a. 30 sq. units b. 20 sq. units c. 15 sq. units d. none...

A:

Q: sin n(4-y)sin(3 – y)dy

A:

Q: The sum of the entries in row 10 of Pascal's Triangle is: O 211 O 102 210 10 acer

A:

Q: Consider the function f(x)=12x^5 + 60x^4 − 100x^3 + 7. For this function there are four important in...

A: Given problem:- Consider the function f(x)=12x5 + 60x4 − 100x3 + 7. For this function there are four...

Q: At what point the function f(x) = 22 +5x+6 22+a-6 has a removable discontinuity? %3D For those who h...

A: This question is related to limits and continuity, we will solve it using given information. 

Q: dy Find using implicit differentiation, for the equation a + = 11 is. da

A:

Q: dy_ y² + xy² 8- dx x'y-x

A:

Q: If f(x) = f (x) „sin(x) e Then f'(0) = ?

A:

Q: Determine the total work done by the force field F(x, y) =. over a particle that follows the path de...

A:

Q: Select ALL possible answers if there is more than one. Which of the following statement's is/are NOT...

A: To solve the following problem

Q: Using an appropriate substitution, 3 the integral S dx equals: V1-4(x-1)2 3 sin-1(2x – 2) + C sin-1(...

A: We can find the integration as below using proper substitution.

Q: Evaluate the limits of the given functions by completing the table of values and its graph and fill ...

A: Let's find. 

Q: MAXIMA and MINIMA Problems Solve the following problems below. 1. A function is given below, what x ...

A:

Q: Evaluate the indefinite integral sin (2)cos"(2)dz 4

A:

Q: of the region bounded by the given curves. * x = 0, y = 0 b. (2,1) с. (-2,1) d. none of the choic

A:  

Q: If f(x) 3 cot lr+ 4, then find the value of f'(-1) is > 8 m IN O O

A: Solve the function

Q: QIAnswer the following equation ,your answer should be like :(x=4)(y=9)(z=6)? * .write it in the sho...

A:

Q: Find the Jacobian of the transformation x = r cos θ, y = r sin θ.

A:

Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)   =14+3+83...

Q: 144. Identify the length of the curve y = x over the interval [2,6] 49

A:

Q: fcac) fCre)ニ2x+5

A:

Q: Find the value of f' () if f(x) = 2csc3x. 15 Your answer

A:

Q: Using an appropriate substitution, 8tan-1x the integral J dx equals: 1+x2

A:

Q: 3. +4 Use the ehain rule to find devinitine

A: Here we have, y=x2-22x3+44 Differentiate with respect to x,   

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A:

Q: Which of the following best describes the function below? S (x)={** ifrso l-r' if 0<x ifx<0 A. Conti...

A:

Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

A:

Q: Sa2 – 6x +1, x 6 Evaluate the following limits for h(x) = and Justify your answer. (i) lim h(x) = (i...

A: As per the guidelines when multiple sub part question are posted in single pic then we are supposed ...

Q: de spaces in characters. * 4 Find the value of f'(-1) if ƒ (x)=- (3r² – 2.r + Your answer

A: Topic:- derivatives

Q: i. Comment whether the sequence is Converges or diverges. ii. Obtain the first five terms of that se...

A: We know sequence is convergent when limit of sequence is finite

Q: Using integration by parts, the integral 2 f cot-1 x dx equals: 2 x cot-1x+ In|x² + 1| + C - x cot-1...

A: Given problem:- Using integration by parts solve 2∫ cot-1(x) dx 

Q: Trace the curve of the following equations by giving the a. Intercepts b. Symmetry c. Vertical Asymp...

A: Equation of a curve is giveny2=2x4-5x3+3x2+4x-20x2-3x+2

Q: dx x In x A 1 lnxl+ C C In I In xl + C 3 B 3 In I In x I+ C D ! In I In x I+C 3 A В C D E None of th...

A: I have stated the used formulas in the solution.

Q: -1 to be continuous at s 1. -1 Define f(1) in a way that extends f(s) (1)=(Type an integer or a simp...

A:

Q: Consider the parallelepiped with adjacent edges u = 9i + 6j + k v = i+j+7k w = i+ 6j + 6k Find the v...

A: The given equations are,  u=9i+6j+k v=i+j+7k w=i+6j+6k.

Q: 2x3+3x dx x*+3x2 C A 2 In I x4 + 3x² I+ C In I x4 + 3x² |+ C In Ix4 + 3x? I + C - In Ix* + 3x? | + C...

A:

Q: for power substitution method, next step is * . For S(y + 2) /2 – 3y dy - (u² + 2) (2 – 39)")}(3u'du...

A: Find out the correct power substitution. 

Q: Which integral would represent the area shown below? The function is f(x) = 2x + 2. 8 6 4- 2- 0.5 1 ...

A: