Find the lines that are tangent and normal to the curve at the given point. x²y? = 100, (-2,5) The line tangent to the curve x-y = 100 at (- 2,5) is y = x+ 10 . The line normal to the curve x y = 100 at (- 2,5) is y= |||

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A:

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension. 

Q: I = Sin 52 ()

A:

Q: Minimize 2x? + 4y, subject to the constraint 82 - 4x- 3y =0. The minimum value of the function is- (...

A: Method of Lagrange Multipliers :            Solve the system of equations                         ∇f...

Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex an...

A:

Q: z+2 dz I cot (z?+4z-3)

A: ∫z+2cot(z2+4z-3)dzSubstitute u=z2+4z-3→dudz=2z+4→dz=12z+4du=12∫1cot(u)duWe know that cot(x)=cos(x)si...

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: Determine whether the series converges; if so, find its sum. Otherwise type N in the blank. 00 1 L K...

A: The given series is sum of 1/[k(k+2)] ,k=1 to infinity.

Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use...

A: We have to show that x is the solution of the third-degree polynomial equation. The real roots are a...

Q: 3y(x^2-1)dx+(x^3+8y-3x)dy=0 when y = 1 and x= 0 solve  solve using exact equations (diff eq)

A:

Q: Find the solution of the given initial value problem in explicit form. sin(2r) dr + cos(5y) dy = 0, ...

A: Find your answer below 

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A:

Q: Compute the average of f(x) = 6x2 + 4x - 5 on the interval 2, 4. %3D Find a value c in the interval ...

A: Average of f(x) in the interval [a,b] is given by f(b)-f(a)b-a

Q: For what function M(x,y) will the differential equation M(x,y)+(x² +x)dy = 0 be exact? а. 2ху — у c....

A: Given:M(x,y)dx+(x2+x)dy=0

Q: Let /(x) = 2x- 3x2. (a) Graph the function for x E [-1,5] %3D (b) Compute f (2) and f (2). (c) Write...

A:

Q: O 2ax-X Sa — х dx Jse gamma or beta laws

A:

Q: ons whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each deriva...

A: We have to choose the correct answer from the given options according to the given information

Q: What is the particular solution of the linear differential equatio y' = x° – 2xy; when x = 1, y = 1?...

A:

Q: Find the area of the region bounded by the graphs of the equation y = x and y= x².

A:

Q: Determine whether the seavence converges dive ges. If it conveges, find the or

A:

Q: The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are g...

A: Given data are,  

Q: Determine the values of the trigonometric functions of 0, where sin 0 = and cos 0> 0. 13 cos 0 = (Ty...

A: Given query is to find the value of 6 trigonometric functions.

Q: 9. 10. 10+ 12-10

A: Topic:- function   

Q: Problem 5 Find the four points Gaussian quadrature formulae given by Roots, ri Coefficients, Ci 0.86...

A: We want to find integral of the function. 

Q: dy = ay + b whose dt Write down a differential equation of the form 17 as t→ oo. 18 solutions all ap...

A:

Q: need

A:

Q: 5. Find T, N, and xfor the plane curve r(t) = (t2, sin t –t cost,cost +t sin t); t > 0.

A:

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact ...

A:

Q: х4 + х3 + x? — х+1 x(x² + 1)²

A: To find out the partial fraction decomposition of the function given.

Q: z+2 dz cot (z²+4z-3)

A: To evaluate: I=∫z+2cot(z2+4z-3)dz⇒z=12∫2z+4cot(z2+4z-3)dz...(1)

Q: 12 Find the arc length of y = In(1 – a2) on 0 < æ < 19 No decimal entries. Find the exact value. L

A:

Q: Given the space curve r(t) = (t, 2e", e²²), find the tangential and normal components of acceleratio...

A: The tangential component of acceleration can be found by using the formula r'(t).r''(t)r'(t) The nor...

Q: Question 13 Evaluate: (6x2– 6x + 6) dx A 10 96 12 - 16 E None of the given choices

A:

Q: Consider the region bounded by the graphs of y = ax", y = ab°, and x = 0. (b > 1. See Figure.) (a) F...

A:

Q: Locate and classify all extrema in the graph. (By classifying the extrema, we mean listing whether e...

A: Given:    Graph is given.

Q: Find the lines that are tangent and normal to the curve at the given point. x²y? = 36, (1,6) %3D

A: We will find first slope of tangent and then from the slop and tangent and point will find a equatio...

Q: x² – 21x + 54 - lim x → 3 х — 3 - II

A: x2-21x+54=x2-18x-3x+54=x(x-18)-3(x-18)=(x-18)(x-3)

Q: A delivery company requires that any box delivered must have a length plus girth (distance around) t...

A: NOTE: Refresh your page if you can't see any equations. . girth is g=2x+2y and the length is z the l...

Q: a. (2xy – y)dx+ (x² – x)dy = 0 b. 2xydx + (y? + x? )dy = 0 c. 3y(x? – 1)dx - (x° +8y – 3x)dy = 0 d. ...

A:

Q: ,3 ws de determine the percentage change in y when w increase by 2%, s decrease 2. If y = by 3% and ...

A:

Q: 1 xV1- (in x)? (In x)²

A:

Q: How did he get the value inside the circle? 2も elt b 3/4 34-1 2/4 314 /4 3/4 to 2

A: The given problem is solved below in detail.

Q: 8. f(x)=3csc(x-x) f(x) Amplitude Period Vertical Shift: Horizontal Shift

A: Solution is here

Q: the strong Allee effect is a population that satisfies rz (5 - 1) (1 – ), dx | dt A where 0 < A < K....

A:

Q: Find the derivative of the given function at a given number. 1. y = 3x² - 2 at f'(1)

A:

Q: /6х — 22

A: We will evaluate the given integral as shown below by using trigonometric substitution

Q: Determine whether the series converges using the Ratio test. The series converges eTextbo diverges

A:

Q: Evaluate the following indefinite integral Use C for any constant of integration 81 x1° dx =

A: The objective is to evaluate the integral. 

Q: If 1=- and V= 250 volts, R = 50 ohms. Determine the change in I resulting from an R increase in 1 vo...

A: Given I=VR   , V=250 volts     , R=50 ohmswe want to determine the change in I when   ∆V=1 volt  ,  ...

Q: Solve the logarithmic equation for x : log2 (x - 2) + log2 (x - 3) = 1

A: