range of the function. (a) If f(x) = 3x + 4, find the image of 4. (b) If f(x) = 7x + 5, find the image of -1. %3D (c) If f(x) = 4x + 1, find the pre-image of 13. %3D (d) If g(x) = 2x + 5, find the pre-image of 15. (a) Let f(x) = x + 4 be a function defined in the interval -5 sxs 5. find ff-2), f(21 f(3), f(7). (b) If g(x) = x² + 5 defined – 6 5 x5 7, find g(2), g(7), g(8). (a) (a) A function f: N→ N is defined by f[X) = x + 3, is f one to one and onto or both ? What is the pre-image of 100. anta Excel In Opt. Mathematics - Book 9

Q: Use the integration by substitution to find the integral –6x² – 4 dx . (7³ + 2x)²

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integral. (Hint: factor the den...

A: Given:           ∫3x+17x2+9x+20dx     Applying partial fraction, we get:         3x+17(x+4)(x+5) = A...

Q: Evaluate the integral below using any appropriate algebraic method or trigonometric identity. T/2 1 ...

A:

Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

A:

Q: Solve using fragmentation of fractions 1 dX x(х — 1)?

A:

Q: Given a function whose graph is shown below. The function is continuous on(-1,0]. 14 Always True Som...

A:

Q: Q3: Find the solution of x.y and z by using Gramer's Rule 2x 4y = 6 x+y+z 1 5y +72 10

A:

Q: Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic equation for C = 15 a...

A:

Q: EX+ Prove that [X Ju cx)] = x'Jr-, cx) Solp 2. ヘャut 2m+2V (-1)" X 2m+V (m!)P(m+v+1). neno 2m+2U-1 (-...

A: Property of gamma function: Γ(m+1) = mΓ(m) ............. (1)

Q: During a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the first 4 hours, at a ra...

A: We have to find piecewise defined function.

Q: A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pe...

A:

Q: Problem: Find the answer following of the alittrential equation. d=2 tan(a) Secix) -y"sinca)

A: Given:    y'=2 tanxsecx-y2 sinx

Q: For sets A and B, define A+ B = {a +b: a € A, b e B}. (a) Prove that if A and B are open, then A+ B ...

A: Let X be the topological space and A,B⊆X where A and B are compact Let {Xα}α∈I be and open cover of ...

Q: Find a formula for the nth term of the sequence in terms of n. 1 2 22 23 24 20' 25' 30' 35' 40

A:

Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. 00 Σ 4 n = 1...

A:

Q: the following ordinary different is nonlinear? = of them (4) – 2y = 2x – 3y u(4) – x³ y" – 2y' = 2x ...

A: We have to choose the correct option according to the given information

Q: Example 2. Find the derivative of the following with respect to x. x" +1. (iv) x-5 (i) x12 + 7, (ii)...

A:

Q: Suppose that f(5) = 3, f'(5) = 7, g(5) = -6, and g'(5) = 1. Find the following values.

A:

Q: Q1:B/ Use l'Hôpital's rule to find the limits lim x-1 In x, x-1

A:

Q: e Does the series E converge or diverge? 8n n=1 1+ e

A:

Q: The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5 inche...

A: Given problem:- The sides of a cube are found to be 6 feet in length with a possible error of no mor...

Q: I. Evaluate the following limits by constructing the table of values. 5. lim tanr 1. lim 3" 2. lim 5...

A:

Q: A5.5-foot-tall woman walks at 4 ft/s toward a street light that is 16,5 ft above the ground, What is...

A:

Q: Find the area of the given region using any method. 1 y = 9 - x2 y 1.5 1.0 0.5 -1 1 -0.5

A:

Q: Find the derivative of the following exponential and logarithmic functions: (i) ecosx-sinx ii. In(3x...

A:

Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5, ...

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)

Q: sinrdr In(cosr – 3) | cosr -3 A cosr – 3 B In (cosr – 3) In (cosr – 3) cosr – 3 D sinr E) None

A:

Q: 3 Find lim s-2- \s-2 s²–4/

A:

Q: non m Q4) Solve the D.E= %3D dx ya

A: Differential equation

Q: Number of phone surveys A research institute conducted phone and mail surveys. The total cost of con...

A: topic - linear function

Q: Johnson's Household Products has a division that produces two sizes of bar soap. The demand equation...

A:

Q: Given a function whose graph is shown below. The function is continuous on(-o, -5). Always True Some...

A: from the given graph we see that the function is not contineous at given region so given is Never tr...

Q: or thG following gr OGLOW.

A: Example (for concepts):

Q: 1 Find the two points on the curve y=- at which the tangents have as slope of -.

A: Given,            The curve y=1x at which the tangents have as slope of -12.To find : The two points...

Q: Given a function whose graph is shown below. -5 -1 2 3 4 The function is continuous on (1,5). Always...

A:

Q: Can you please answer both

A: see below the answer and calculation

Q: During a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the first 4 hours, at a ra...

A: Depth of the snow= snow rate*(time) 0≤t≤4f(t) = (2 inches per hour)*(time)f(t) = 2 tfor the next fou...

Q: represent the total number of trees in the forest, let h represent the number of hickory trees, and ...

A:

Q: Find the Taylor polynomials of order 0, 1, 2, and 3 generated by f at a. f(x) = /x , a=4 The Taylor ...

A: f(x) =xf0(x) = xf0(4) =2f1(x) = f'(x) = 12xf1(4) =14f2(x) = f'' (x) = -14 x32f2(4) =-132f3(x) = f'''...

Q: Solve for t e2t+ 4et + 4= 0 e2−4t + 5 = 20

A:

Q: A limestone stalactite grew in length at a rate of – of a millimeter per year. At this rate, how man...

A: Given the limestone is growing at a rate of 18mm per year i.e. 0.125 mm every year

Q: (a) 2(x- 3) + 11 = 6- x x-4 (b) 3+x 三 3 (c) x2 - 7x + 6 = 0

A:

Q: x3 if x 1

A:

Q: If f(r) is positive then for all 1 <I<2, we have So f(z) dz 7. Select one: O True O False

A: If f(x) is positive then for all 1≤x≤2, we have ∫07f(x) dx≥7

Q: solution

A:

Q: 2 -a - 12a? + 70x – 60. Find all local extreme values of f(x) at The FIRST local extreme value, movi...

A: Given :- f(x) =(2x3/3) -12x2+70x-60 find:- All local extreme values of f(x)   

Q: The solution of the following linear differential equation xy' – 3y = - is y(x) = 2x – 1+ ce¬2x y(x)...

A:

Q: Two people sweep the floor. The table gives their sweeping rates, in square yards per minute (yd²/mi...

A:

Q: tion f(x) = x cosx.

A:

Q: The bus took 7 hours 26 min to travel from Bloemfontein to Grahamstown. Talculate the average speed ...

A: Distance = 597km  time = 7 hour 26 min                                                =  7.433hour