expand using the binomial theorem. simplify (a+b)^2 (2x^2 -1/x^2)^4

Q: g(x)=x5bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: Given a=15, b=12 & c= 15

Q: T/6 6 tan 2x dx

A: In this question, we need to evaluate the given integral.

Q: Use the Laplace transform to solve the given initial-value problem. y'' + 2y' + y = 0,  y(0) = 1,…

A: A detailed solution is given below.

Q: f arctan y dy 3 f

A:

Q: Question 5 limx→→+∞ (1 + ¹)² O ll SO III OIV O Not Indeterminate

A: Please mention also what the first four options wants to represent here ...as correct answer is e .

Q: Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t): 8 S 8 - a) b) (s+2)2+16 2s2+18 (S-2)2+16 252418 c)…

A: 17) To evaluate: L(2e-2tsin 4t-0.5cos 3t)

Q: Find the critical values (if any) of the given functions. With solution please.

A:

Q: Exercises A write the 1st 4 terms 1 2. 1:4 운 은데linity 2. 을 , I 141

A: Given that the series is

Q: A drink can, in the form of a cylinder, needs to have a volume of 750 cm³. The material for the top…

A:

Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

A:

Q: 5) An isotope of lead decays according to the function remaining, in grams, after t minutes. a) What…

A:

Q: 5. Find the length of the curve = = = (1 ²+2) X=- 3 9 0≤ y ≤ 4

A:

Q: Exercises A write the 1st 4 terms 1. >. र 2641 0:4 [(-₁)^(²) 2. 2. I

A: Given that infinite series is

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

A:

Q: 52.416 X 0.73 157248 +C

A:

Q: Find the area of the region under the graph of the function f on the interval [4, 5]. 9 f(x) = -2²/2…

A:

Q: * Define this property L (f(t)eat) = F(s-a) Second shifting property O Linearity property O…

A:

Q: a. [8t7dt dx b. S sin x tanx C. d. S [ 26* dx 3d8 √8

A:

Q: f(x) = 4x5 (12x² + 15x + 3)

A:

Q: Six 2 CSC ² 2x - x cos 2x) dx

A: We know, ∫cosmx dx= sinmx/m  ∫sinmx dx= -cosmx/m  ∫cotmx dx = ln|sinmx|/m  ∫csc²mx dx= -cotmx/m…

Q: Find the average rate of change of from y = x³ - 2x + 3 from 0 to x = 3. -

A:

Q: Differentiate f(x) = f'(x) = 2 ax with respect to x. Assume that a and k are positive constants. k+x

A: To differentiate fx=ax2k+x with respect to x. Assume that a and k are positive constants.

Q: -4x 2. Determine an equation for the tangent to the curve y = (x+3)² at x = -2.

A:

Q: A rectangle is enclosed by the coordinate axes and the line 2y + x - 5 = 0 Determine the length and…

A:

Q: Write the matrix below as a product of elementary matrices 1 2 3 235 1 05

A: The objective of the question is determine elementary product of matrices ,of the given matrix

Q: Given y(t) = e-³tu(t) u(t + 3), where * denotes convolution operation. The value of y(t) as t → ∞o…

A:

Q: 12) The formula of the particular solution yp of y(4) + 4y"=3 sin(2t) - 5cos2t, is: a) yp= Asin(t) +…

A: The given differential equation:y4+4y''=3sin2t-5cos2t.We need to find the formula of  the particular…

Q: Differentiate the function with respect to the independent variable. x f(x) = 4x cos+ + cos f'(x) =…

A:

Q: () without a calculator. We will do the followings: (1)- 1.2.3.4 7.6.5.4 1.2.3.4 I will introduce a…

A: Using definition of combination

Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

A:

Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A:

Q: y" + 3y = 18x², y(0) = -3, y(0) = 0

A:

Q: Q14) The solution of y'" + y = 0 by using power series method, is: a) y(x) = 40 + a11- + ...) 41 51…

A: 14)    Given differential equation y''+y'=0 ......................(1)    We can substitute…

Q: x 5√x ³ + 4 dx 3 Lx5

A:

Q: Question 3 A container with square base, vertical sides, and open top, is to be made from 3,000 ft²…

A:

Q: Which of the following describes a function? 1. y=x² +1 x=y² +1 1 I only Oll only I and II Neither I…

A: We have to tell about which is showing a function

Q: Which of the following functions is entire? For each, justify. = 2(32) ƒ(z) = 2'

A: Given :   f(x)=2(3z)

Q: uestion 4 (a) Solve the following: 4x*dx (b) Explain with the aid of a sketch how this value can be…

A: A detailed solution is given below.

Q: Use the Laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t,    y(0) =…

A:

Q: 8 1 ₁ }(s) = = nº n=1 Show that finding the value of the Reiman Zeta for (2) is just the value Basel…

A:

Q: f(x) = 3x² - 5x+21

A: SOLUTION-

Q: 2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately…

A: Let  at time t the amount of plutonium is  A(t)

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

A:

Q: Question 4 (a) Solve the following: √4x¹dx (b) Explain with the aid of a sketch how this value can…

A:

Q: Investigate if the integral is convergent or not. Justify your answer.

A: Given:     ∫1∞dx1-x   Substitute u=1-x→dudx=-1                dx=-du   =∫1∞-1udu

Q: At which point/s is the absolute value function not differentiable? x = 0 The absolute value…

A: Above question is solved.

Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √√x + 4 and x - 2y +…

A:

Q: Let f(x) = 2x² -5x - 7. Expand and simplify: f(x +h)-f(x) h =

A: The answer is given below: