Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x = t + 2,  y = 1/t,    t > 0

Q: 2 ext 5. g(x) = .x+1.

A:

Q: Sin x y = 2+Cos x

A: Given, y=sinx2+cosx We have to find the derivative of the above function.  

Q: Find 16. f t sinh mt dt 17. e sin 30 d0 18. ecos 20 de

A: detail solution is given below.

Q: If f(x) = (5x +6) find f'(x). Find f'(3).

A: topic - derivative of a function

Q: I have two "given" pieces of information. Given #1: f(8) = -6 Given #2: First attached image. H...

A:

Q: (DE- 6D + 25)у %3D0 y =

A:

Q: dx x2 – 64 First, rewrite this with partial fractions: S, da = f 1/(x+8) dx + [ 1/(x-8) dr = log(x+8...

A:

Q: Determine whether the alternating series converges. 5ln k E(- 1* k k=3 O The series diverges. O The ...

A:

Q: (e* + y)dx + ( 2+ x+ ye' )dy =0

A:

Q: Determine the exact coordinate of a point at a distance of 4 units from the origin in the second qua...

A:

Q: How fast is the volume V of a rectangular box changing when its length L is 10 ft. and increasing at...

A:

Q: 13: 3. y = V(4x + 3)3

A:

Q: Solve the equation dy y° – y, - dx? dy giving that dx 0 when y = 1 and y = 2 when x = V2. %3D

A:

Q: -Divide (3x3-2x²+12x-9) ÷ (x²+2) . state answer using a correct division

A:

Q: (0, 1) (0,0) (1,0) FIGURE 0.1. The triangle T of the problem. Consider the triangle T with vertices ...

A:

Q: Name and graph the following quadratic surface. 9x2 + 4z2 – 36y = 0

A: For (b) Sketch of z=9-x2-y2: The graph is a paraboloid.

Q: dy (x+2)² x² - 4 2y dx'x -4

A: find the solution of given differential equation. dydx+2yx2-4=x+22x2-4

Q: 13. Find the value of t in the given interval at which the given curve is not smooth. r(t)=(5cost- c...

A: Given curve: r(t)=5cos t-cos 5t, 5sin t-sin 5tt interval: π4,3π4

Q: (e*+ y)dx + ( 2+ x + ye )dy =0

A: Given, (ex+y)dx+(2+x+yey)dy=0 expand the terms to get the solution Note: xdy+ydx = d(xy)

Q: Solve the given differential equation. x?y" + xy' + 36y = 0 y(x) : ,x > 0

A:

Q: VI APPLICATIONS 1. Solve for the orthogonal trgectories y2= 4x (1- kx) %3D

A: A detailed solution is given below

Q: cos°( VJ) y ycsc y

A:

Q: Set-up the integral to calculate the area of a region bounded by x-y=3 and y=x2 -6x+9 ? A dy dx x2- ...

A: Graph:

Q: ( 3x²y + eY )dx + ( x³ + xe' – 2y)dy=0

A:

Q: For the given parametric equations, find the points (x, y) corresponding to the parameter values t =...

A: Given: x = t2 + t       ,     y = 3t+1  values t = -2, -1, 0, 1, 2 

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,...

A: Given: I=∫-∞122x-32dx   We know that the power rule: ∫xndx=xn+1n+1+C ; n≠-1 And ∫c·fxdx=c·∫fxdx

Q: Find the derivative of f(x) = -6x 10x10 f'(x) =

A: This question is related to derivatives.

Q: The magnitude of three vectors a, b, and c form a right triangle. Given the equation, what is the va...

A:

Q: () 2. Use the Squeeze Theorem to evaluate lim r COS

A: Given problem:-

Q: Find DE 576 || x9 Type your answer without fractional or negative exponents. Use sqrt(x) for sqrt(x)...

A:

Q: 17. Find all local maxima, local minima, and saddle points for the function: f(x, y) = x³ – 6x

A:

Q: f(t) = e-5t

A:

Q: Evaluate the indefinite integral sin' t cos tdt %3D + C

A:

Q: How close to -2 do we have to take x so that the following is satisfied? (Give the largest possible ...

A:

Q: Evaluate the indefinite integral ²v cos vdv = %3D + C

A: As we know that; The trigonometric identity: sin2x+cos2x=1 The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; ...

Q: Test the series below for convergence using the Ratio Test. 97 n! n=1 The limit of the ratio test si...

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

Q: x + 3x – 1 lim V4r6 – 2x エ→ーx 2.r

A: We have to find limit

Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We ...

Q: 1. Find all possible points of discontinuity and classify each discontinuity as removable, jump esse...

A:

Q: If > uk and > v% are convergent series, then > (uk + v%) and 2(uk – Vk) are convergent series and th...

A: First we take partially fraction then we use sum of GP. 

Q: Test the series below for convergence using the Ratio Test. n² 0.8" n=1 The limit of the ratio test ...

A:

Q: When playing American​ roulette, the croupier​ (attendant) spins a marble that lands in one of the 3...

A:

Q: 2. Evaluate the fellowing Integrals:- e dx dx ans (z a.

A:

Q: Find the derivatives of the following Trigonometric Functions and Inverse Trigonometric Functions:

A: y = ex sin-1xdydx = ex ddx(sin-1x) + sin-1x ddx(ex)        = ex 11-x2 + ex sin-1x 

Q: Stan (y-t0) dy ( α年

A: Our Aim is to evaluate the integral given below:-∫tan y-π4 dy-(i)

Q: dy Solve: (e +e-²)- = y? (separation of variables) dx

A: We want to solve the given differential equation.

Q: You are given the graph of a function f. 1 Determine the intervals where the graph of f is concave u...

A:

Q: d²y 1. 5 dx - 6y = 0 y(0) = 2; y'(0) = 4 - %| dx² d²x(t) 2. ·+ w?x(t) = 0 dt2 x(0) = A; x'(0) = vo %...

A: I am attaching image so that you understand each and every step.  

Q: (e* + y)dx + ( 2+ x + ye )dy =0

A:

Q: Solve S0lve: とマ ans

A: Given:     I = 4∫0π2 ∫0∞ e-v2v dv dθ