Q3/ Find the limits x*+x²-2 1. lim X-1 -1 Vx+2-1 2. lim X-1 x+1

Q: Use the properties of the derivative to find the following. r(t) = ti + 5tj + t?k, u(t) = 5ti + t?j…

A:

Q: Consider the function f(x) = cos(3 x). (a) Give the derivative of this function. f'(x) = | (b) Find…

A:

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

A:

Q: If f(x) = sin (a*), find f (x) Find f'(5)

A: Given function is f(x) = sinx3 we have to find the first derivative of f(x) that is f'(x).

Q: Find F as a function of x and evaluate it at x = 2, x = 4 and x = 9. F(x) = (t° + 8t – 4) dt F(x)…

A:

Q: Find an explicit formula for an. 15) 0, -1, 0, 1, 0, -1, 0, 1, . . .

A:

Q: Find the general solution of the differential equation dx = xin (xy)

A:

Q: 9. Verify the identity 1 1 = 2 sec² x 1-sinx 1+sin x

A:

Q: Use Laplace transforms to solve the following initial value problem S y( (t) – y(t) = 8 (t) y(0-) =…

A: We need to find out laplace transform of the initial value problem, which is described in step 2 .

Q: Find the general solution of the given ODE: dy _ x²y – 4y dx x + 2 (x² y = Ce2 = ce) (x² = Ce2…

A:

Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: 3 1 - dx 2 2. cos sin X

A: solution:-∫cos4xsin3x1x2 dxlet 1x=t-1x2dx=dt=-∫cos4tsin3t dtWe know that the formula  2cosAsinB =…

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

A:

Q: dv 4.)Prove that f -Incosv + Insinv + C sinvcosv

A:

Q: convert csc x/ cos x to sec^2 x/ tan x

A:

Q: Let f(x) = - 5 sec(6x) f (x) =

A:

Q: 12. y" +y = séc' x tan x.

A: Let's find.

Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A:

Q: dr 1/4( In 4) o 1/( In 4) o In 4 In (4) 1/4

A:

Q: 4) 4+ 3+ -5 -4 -3 -2 3 4 5 r -2+ -3+ -4+ 2.

A:

Q: Evaluate the line integral. The simple curve is C is y = x² starting at (0, 0) and ending at (1, 1).…

A: We can solve as follows

Q: Step 1 To find the definite Integral 9 dx by the limit definition, divide the Interval [2, 7] Into n…

A: For the asked steps we can solve as follows.

Q: The equation in slope-intercept form for a line passing through the point (- 3, 2) that is parallel…

A: Topic = Coordinate geometry Correct option = A

Q: 4x 9. sech(2x) dx e

A:

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + = subject to x2 + y…

A:

Q: Write the first four terms of {an}. n + 1 10) an 3n - 1

A:

Q: Write z1 and 22 in polar form. 21 = -36, z2 = V3 +i Z1 Z2 Find the product z1z2 and the quotients 2…

A: Let's find.

Q: Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: To find the smallest distance from the given point to the surface.

Q: Differential Equations Please answer as soon as possible, i'll upvote (a) Find a particular solution…

A:

Q: Find the length of the curve. 8) The spiral = e20, 0 s 0 s Ti r

A:

Q: Given: R. 23 30° A R= 04 v3 02 v3 B.

A:

Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: Give your answer correct to Use differential to estimate the value of y 4.01 V4.01 8. four decimal…

A:

Q: Find the curvature of the curve 7 (t) = (2 cos(t), 2 sin(t), t) at the point t = 0 Give your answer…

A:

Q: dz and dy dz Suppose z is a function of x and y, and tan Vy² + x2 = 2"e®y_ Solve for

A:

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

A: Area bounded by the curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: (4, 4) y= 2x-4 (1,-2) Jsing a horizontal element of area, the area of the shaded region is given by…

A: As required, draw a horizontal stripe as shown:

Q: The volume V, in liters, of air in the lungs during a three-second respiratory cycle is approximated…

A:

Q: If f(z) = 4,/ In(x), find f'(x). Find f'(2).

A: Given function:fx=4xlnxWe need to find f'x and f'2.We will use the following…

Q: P1:

A: Solving

Q: P8: sin x cos x (2 sin x – 1)(sin x + 1)

A:

Q: EXAMPLE 1: Consider the graph of the funetion f given below. Using the given graph, determine if the…

A: topic- continuity of a function

Q: 25 2) V1x-91

A: To evaluate first: ∫dx|x-9| Assume the positive factors and multiply the correction factors:…

Q: n²2" n=1 a) Show that the series is convergent

A:

Q: f(x)=/1+2sin x j. f(x)=e" +4* +sinh(10x)

A:

Q: P1: 2 cos-1 x dx 1xo

A:

Q: Complete the equation. V-14x ). arccos X- 7 = arctan 7 <x < 14 7

A:

Q: P7: x3 + x – 1 x(x – 1)(x + 5)²

A: The given problem is solved below in detail.

Q: sec 1.)S Intanßtanß dß

A: