Find the derivative: y = x [ln(x) - 1] O ln(x) - 1 о O x ln(x) O In(x) O 1 + In(x)

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: Prove that if i and k are relatively prime positive integers, for every positive integer l the…

A: Concept: Number theory: Number theory is an area of mathematics that aids in the study of the set of…

Q: What is the area bounded by the curves y=x2+5 and y=−x2, the line x=3, and the y axis.

A: Topic:- application of integration

Q: ≤ Lºin( Verify that f(x) = sin() is an odd function and use that fact to show that 0 < sin(√√x) dx ≤…

A:

Q: A 200-g sample of a radioctive substance is placed in a chamber to be tested. After 3 h, 140 g of…

A:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: əz дz Find and ax if z is defined implicitly as a function of x and y by the equation ay + +z6+…

A:

Q: Determine if the function f(x) is continuous and/or differentiable at x = 2? x+10 for 2≤x≤2 f(x) =…

A:

Q: Use a graphing utility to graph the equation. Use a standard setting. y = x2 + x − 12   Approximate…

A: The given function y=x2+x-12

Q: 3. A right circular cone has the following dimensions: Radius: R Height: H Then its volume is R²H.…

A:

Q: Determine whether or not the following limits exist (explain why or why not): x² - y² a) lim…

A:

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: To find out the levels of x and y which will maximizes the utility.

Q: Find the value(s) of k that makes the given function continuous. (-x+2 if x < k f(x) = 4x + 3 if k ≤…

A:

Q: 3. Evaluate 622 dV where G is bounded by r+ 2y + 4z = 8 in the first octant.

A:

Q: dy 1+x²)²e³ = -2x dx

A: Topic:- differential equations

Q: The midpoint of AB is at (0, 0). If A = (-5, 4), find B. B is: (

A: Given :A=-5, 4Mid Point of AB=0,0

Q: Find F(s). ℒ{e−8t cos(6t)}

A: To find the laplace transform of the given function.

Q: • III.6 622 dV where G is bounded by r + 2y +4:= 8 in the first octant. 3. Evaluate

A:

Q: Given f(x,y)= x³(x²y³-2y²), find all of the first and second partial derivatives.

A:

Q: Write the equation of the circle centered at (1, 10) with radius 3.

A:

Q: Describe the advantages and disadvantages of using linear scale axes versus logarithmic scale axes…

A:

Q: x + 7x5 +15x4 +32 x³ + 23x² + 25x - 3 (x² + x + 2)² (x² +1) ² 2 dx

A: SOLUTION-

Q: Determine whic 3. The expression log 29+ log 28 + log 27 + log 26 +log 25 - 2 log 5 can be written…

A: We can find the answer as below.

Q: Differentiate the function with respect to the independent variable. 9 h(t) = -t²- +4 h' (t) =

A:

Q: How many square units is the area enclosed by y + 2x - 5 = 0, y = 4x - x² and x² - 4y = 0 ?

A:

Q: aximum profit is d to nearest integer.)

A: Topic:- application of derivatives

Q: (c) Use the WASHER METHOD to set up a (sum of) definite integral(s) that is equal to the volume of…

A:

Q: 1. f(x) = x² − 16x, [3, 10] 2. f(x) = 15 – 2x − 2x², [1, 2] 3. f(x) = 2x³ + 3x² − 12x + 24, [−4, 0]

A:

Q: Given that f(x) = x³h(x) h(1)=2 h'(-1)=5 Calculate f'(-1).

A:

Q: Given = (1 + x -- k) dy da 13 What is the value of k such that y is perpendicular to the curve y =…

A:

Q: Determine if the function f(x) is continuous and/or differentiable at x = 5? x+5 for 5≤x≤5 f(x)= 2x…

A:

Q: dx sin x tanx

A: Here we have to solve only part b

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

A:

Q: Using implicit differentiation, find Provide your answer below: dy dx Content attribution dy dx √xy…

A:

Q: [ (ax + b) c+b) dx = ○ / (ax + b) ² + C O O4a ¹ª (ax + b) ² + C O4a (ax + b)² + C O4 (ax + b) + C 7a

A: You must have basic idea about indefinite integral in order to understand this better.

Q: 4. fx(1-x) dx

A: Given ∫x(1-x)9dx

Q: Use a linearization to approximate tan(π/100).

A:

Q: Determine whether the differential equation (7x² − 2xy + 2) dx + (8y² − x² + 7) dy = 0 s exact. If…

A: Topic:- differential equations

Q: 3. [Arccos 2xdx

A: To integrate

Q: 3 + 2x² √3+2 x2 O 2x 3 - +C X + + 2x + C x3 23³3³ +0 x³ + 2x + C O dx =

A:

Q: 1. f(x) = 3ex +1 2. f(x) = 45x + x45 3. f(x) = 10 sin x + 5 sec x 4. f(x) = x²(2x + 1)

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 1) (4x + xy²)dx + (y + x²y)dy = 0_2) y' - 2y = 5 3)xxx + y = x

A:

Q: Find the interval of convergence of (x - 2)" In (5n) n=2 (Use symbolic notation and fractions where…

A: To find interval of convergence of ∑n=2∞ (x−2)nln⁡(5n) Let an = ∑n=2∞ (x−2)nln⁡(5n) Therefore, an+1…

Q: x3 5x² Find the absolute maximum and absolute minimum of the function f(x) = + 4x + 2 over the…

A:

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

A:

Q: 1. f(x) = 4x² (8x + 1) 2. f(x) = (100x² + 25x)(10x² − 15x) 3. f(x) = (2x + 1)(4x + 3) (5x - 1)

A: Let's solve all given derivative by using product rule.

Q: 3. Let R be the region below bounded by y² + x² = 9 and (y-2)2 + x = 1. (0,3) (a) Set up a (sum of)…

A:

Q: ©√ √16- Evaluate 1 √/16 - 16x2 -doc

A:

Q: Find the following rates of change using a graphical method using the graph shown. a) The average…

A:

Q: hand written pl Let A(0,-2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA) 2. m(PB)…

A: