f(x) = 9x²

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: 5. y³ = 4(y + x²)

A:

Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.

Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.

A: We can solve this as follows:

Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: Find fxy.

A:

Q: Compute the general solution to the second order linear non-homogeneous differential equation: d²y…

A: Given differential equation, d²y/dx²-2dy/dx=8sin2x Corresponding homogeneous equation, (D²-2D)y=0…

Q: Consider the positively oriented surface S₂ defined by the vector function R(u, v) = (u sin v-3, u…

A:

Q: 0 ex [ 224²1 ex + 1 J-In 2 dx

A:

Q: 0.99 6. е.

A:

Q: 3. Find y' and the equation of the tangent line to the graph of In(ay) = y²-1 at (1,1). 11: 11:

A: We have to find y' and equation of tangent

Q: Please fix the mistakes that are in Red for me.

A: Note: Since you have posted a question with multiple subparts we will solve the first three parts…

Q: Consider the matrices shown below: Compute CT-14 CH [142] 31 5

A:

Q: Assume that the given figure is the graph of f'. y in

A: Local Maximum:It is a point within an interval at which function has maximum Value. Local Minimum:It…

Q: Is it possible to solve it without a pocket calculator ??

A: Here to evaluate: t=∫03ds(2.78s+0.8s3)12 The integral can't be evaluated manually.

Q: Evaluate the double integral Jª R where R is the region bounded by the lines y = x and y = 2 and the…

A:

Q: Q1): Prove that: A square matrix B has inverse if and only if determinant of B is not equal zero.

A:

Q: (b) Find the chromatic polynomial of G G

A: The number of distinct ways to color the vertices of a graph with certain number of colors is…

Q: Suppose the position of an object moving in a straight line is given by s(t) = 5t3-712 +9. Find the…

A:

Q: Let f(x) = x²30 Find the critical points c that correspond to local minima.

A:

Q: S x-6 x²+9 dx

A: To evaluate the given integral. ∫x-6x2+9 dx

Q: Assume y = f(x) is a function that is continuous on the real line. Which of the following statement…

A:

Q: Consider the function. 700----14 Identify the domain off. (Give your answer as an interval in the…

A: We need to fill answers.

Q: How to solve dx = 2dy = -2dz.

A:

Q: Find the critical point and the intervals on which the function is increasing or decreasing and…

A:

Q: 2 Let f(x) = 5x4 -/+8√x-3. a) Find f'(x). (b) Find an equation for the tangent line to the graph of…

A:

Q: Find the transition points. y = 15x³ + 360x² (Use symbolic notation and fractions where needed. Give…

A:

Q: Consider the R 2 − R function defined by f(x, y) = 3x + 2y. Prove from first principles that lim…

A: Let's evaluate given R2-R functions limit.

Q: S tan-1 е' 1+4t² 2t dt

A:

Q: dx ylnx dy || y + 1 X 2

A:

Q: Evaluate the following integrals: 4x 6. ₁² x 3x²y²dy dx

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Find the critical point and determine if the function is increasing or decreasing on the given…

A:

Q: Consider the two by two system of linear equations x +3y +2y d) What is the coefficient matrix A? e)…

A: Here we will solve the given system of equations,

Q: of Taylor series for F(x) = Sin(pnx) + ex-p, about

A:

Q: Consider the function f(x) = 4x²² Identify the locations where f has transition points. (Give your…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Find the transition points. f(x)= x(11x) (Use symbolic notation and fractions where needed. Give…

A: Given problem:- Find the transition points.   f(x)= x(11-x)1/3 Find the intervals of…

Q: Find the critical points of f(x) = x³ - 21x² + 144x and use the Second Derivative Test (if possible)…

A:

Q: 1. If F(x) = Le d ex dt, find F(1) and F'(x).

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Q: ff xy dx dy

A:

Q: use the graph of the function √²³ (x³²-6x) dx to explain the geometric meaning of the value of the…

A: Given function ∫03 (x3-6x) dx This below image is the graph of the function

Q: 7) Find the critical point (s) of f(x, y) = 2x³ + 3y² - 9x² - 30y + 12x-3. Then use the second…

A: solution is given below...

Q: S -1 etan 1+4t² 2t - dt

A: Let u=tan-1(2t)⇒dudt=21+(2t)2=21+4t2⇒du2=dt1+4t2 ∫etan-12t1+4t2dt=∫eudu2…

Q: 8. 9. 10.¹₁²(x² (2-y)dy dx π/4 /²x cos y dz dx dy + y² + z²) dx dz dy

A:

Q: etch the region enclosed by y = x²y = √√x,x = 0,x = 1 and find its area.

A:

Q: Q3/ Evaluate four of the following integrals. ( x³+1 sinx cosx dx b. f*+¹ dx c a. S √1+cos2x x²

A:

Q: 4 The terms of the Maclaurin series of the function f(x) = - -x are given by

A:

Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A: Given function f(x)=3+12x-x2 To find critical points we need to differentiate the function f'(x)=0…

Q: 4. Evaluate (x - 1)(x + 1)da using the Fundamental Theorem of Calculus.

A:

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2