(b) State the range of f for the domain given in part (a). f:A B f(x)=(x-1)²+4. (c) Define the set B so thatf is bijective. 1. Consider the function la) Given that A=eR/x2a},state the smallest value of a for which 1s injective. of f for the domain given in part (a).

Q: Simplify by rationalizing the denominator. 1

A:

Q: 1 Compute 7' (t) where 7(t) : t+1

A:

Q: Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

A: We use integration to find the area.

Q: Tan -30  find the exact value of each trigonometric function

A: The given trigonometric function is: tan(-30)

Q: The independent variable(s) of the equation Urr B- uy + aug is/are ох, у a, ß о и, х, у

A: The given differential equation is:uxx=β2uy+αux

Q: Given: x'(t) + 2y(t) = - 1 where, %3D x(0) = y(0) = 0 x(t) - y'(t) = 2t %3D Find : u(s) = L{x} %3D (...

A: I have stated the used formulas in the solution

Q: Evaluate f (t) given t = 0 for s-1 F (s) = (s+3)(s-5) 1 e e3 0 1 3. 15 4 3

A:

Q: 2. The rate at which a phase transformation proceeds depends on the time t and the dt transformed vo...

A: Rate of Phase transformation is gievn bydydt=4kt3(1-y)We need to find y as function of t.  

Q: (1, 0 2 L (2) = + e (-!) te-2s (s-1) S (음 + 1) O. e2 L (y) = -2s e - s2 ( (s-1) °L (y) = -2s e (s+1)...

A:

Q: О 10 O 5

A:

Q: Given a differential equation with certain conditions y (to) = or yfk) (to) = Yk = Yk' the largest p...

A:

Q: Fill in the blank with the appropriate word, phrase, or symbol. When the denominator of a fraction c...

A:

Q: (1) (a) Solve the following: (i) 2 =! (b) The population of the world in 2015 was 9.75 billion peopl...

A:

Q: Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA –...

A:

Q: Evaluate the following integral by using method of substitution: 1/ (1+9x^2) dx Limit: 0 to 1/√3

A: NOTE: Refresh your page if you can't see any equations. . substitute  ............put it back in ...

Q: A 300-gallon capacity tank is originally filled halfway with a brine solution that contains 2 Ibs of...

A: Given:   Data is given

Q: Subtract. Simplify by collecting like radical terms, if possible. 4/5 - 10 /5 4/5 - 10/5 =O (Type an...

A: This can be solved as follows:

Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is pro...

A: Half-life = 0.693/Decay constant(lambda)

Q: Find L{(1 – t) (3 + 2 sin 5t)} . 3 2s 10s - 82+25 (s2 –25)² - 10 20s 을 + - - s2+25 (s² +25)² 3 3 10 ...

A:

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32 ft/...

A:

Q: 196 The number is because it be expressed as a ratio of two integers.

A: Given number is    196

Q: true ? following which of the is 9. In finite rey union finite set is finite set. of 6. The union of...

A: (b). If A and B are disjoint denumerable sets,then A∪B is also denumerable.

Q: Given the differential equation dæ? + y = e-bª sin(æ) Propose an appropriate particular solution. Yp...

A:

Q: page 4. INDICES AND SURDS PAPER 1 J2014 ven that 2**× 4vx gr-y = 1 and 3*+y =, find the value of x a...

A:

Q: Evaluate the given indefinite integral. Indicate u, n, and du. xdx 3-x

A:

Q: each

A:

Q: PAPER 1 4. INDICES AND SURDS N2014 page 25 (a) Solve the following simultaneous equations. 5* 25-2 =...

A:

Q: 3t L cos 2tdt 1 s- 3 (s – 3)? + 4 s[(s – 3)' + 4] O A.) O B.) s- 3 4 (s – 3) + 4 s[(s – 3)? + 4] C.)...

A:

Q: A particle that moves along a straight line has velocity v(t) meters per second after t seconds. How...

A:

Q: obtain the general solution. xcos^2 ydx +tanydy =0.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: Find the exact length of the curve. 4 1 X = 1<y< 3 + 8 4y2"

A: we will find the exact length of the curve.

Q: Find L(y) y" - y = 1 0st< 2 It+1 t2 2 y(0) = y'(0) = 0 °L (1) = + +] -2s e %3| s(s2-1) s2-1 -2s L (y...

A: The given differential equation is: y''-y=1         0≤t&lt;2t+1t≥2;                y(0)=y'(0)=0There...

Q: (a) Define what it means by 2 for y = f(x). %3D

A: Topic:- calculus

Q: (2) A study indicates that spending money on pollution control is effective up to a point but eventu...

A: The percent of pollution removal when x million dollars are spent is given by  as below: a. We need...

Q: Solve the following and show your complete solution Find Taylor Series Expansion and Compact form of...

A:

Q: 1. A through of length L has a cross section in the shape of a semicircle with radius r. When filled...

A: Given: A semi-circular through ,filled with water.  V=L[0.5πr2-r2arcsin(hr)-h(r2-h2)12]L=10ft , r=1 ...

Q: Find f'(a). f(x) : Vx + 9 f'(a)

A:

Q: ind the general solution : a csc() – y] da + ædy = 0 X CSC x = e (csc + cot ) In (ese + cot ) In = c...

A:

Q: For a given function, F(t), the Laplace transform is obtained by integrating the integrand e-st F (t...

A:

Q: "dog 1) ]* dx 8. x(1+log²x) 2

A:

Q: Scos* y sin ydy

A: Given problem:- ∫ cos4(y/2)sin(y/2) dy

Q: dy If the differential equation dx = y? ; y is solved via the substitution z = y1, the resulting equ...

A:

Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: A spring has natural length 28 cm. Compare the work (in J) w, done in stretching the spring from 28 ...

A: Given:- A spring has natural length 28 cm. Compare the work (in J) W₁ done in stretching the spring ...

Q: evaluate

A:

Q: P2.B: Evaluate the integral: (x+1)/2 J (x – 1)5/2

A: The given integral is (x+1)1/2 /(x-1)5/2.

Q: ) A stone is dropped into a pond and sends out a circular ripple whose radius increases by 5 cm/seco...

A:

Q: 5. Express the given function using unit step function: * [t f (t) = 0st<4 2 , t24 O A.) f (t) = t -...

A:

Q: [5an28 elan 20 sec 2 Bdß 1. e²x +2e* - dx e* +1 2.

A:

Q: 3xy? dx t (3x?y t qy% )dy

A: