Find 2 dr if y=1-t² and x= 4+² dx

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.

Q: If the population of a city is 155,000. If the population declines continuously by 5% per year, what…

A: Let P be the population after t years

Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: Find values of x and y such that  fx(x, y) = 0 and fy(x, y) = 0  simultaneously. f(x, y) = 7x3 −…

A: This question is based on Partial differentiation.

Q: 1- Use the shell method to find the volume of the solids generated by revolving the shaded region…

A:

Q: 2. Find the general solution o- = y(1+e³) 1 له 342433434 11 11 1 "싫

A:

Q: zu 00{ " + uc}

A:

Q: Particular solution of y" - 5y'=x-2, when x = 0, y = 0, y = 2

A:

Q: Evaluate (ƒ¯¹) '(2) for the function 3 2 f(x) = √√√x³ + x² + x + 1. Explain your reasoning and write…

A: The given function is  f(x)=x3+x2+x+1

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(2,0,2) on the…

A:

Q: Consider the functions z = 7 e* In y, x = In (u cos v), and y = u sin v. ex əz dz (a) Express and as…

A: This question can be solved by the concept of partial derivatives.

Q: Let f be continuous on [a,b] and differentiable on (a,b). Prove that if f'(x)>0 for all x=(a,b) then…

A:

Q: 1.) Find the area of the region bounded by the curve ya 12 and the lines y=o, y=x, x=2.

A:

Q: V. En el siguiente ejercicio obtent 1 + Int 1 - Int

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4. According to the following table, what is the limit of this function as x approaches 0? X -.01…

A: From the table, it is clear that: limx→0-f(x)=2&limx→0+f(x)=2

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = xy + 2y², Po(-7,-9),…

A:

Q: You made a mistake in the calculation. The final answer is 31,972.5. But thanks for the process.

A: Silly mistake in calculation, we provide correct calculations

Q: Find xer2 dy if dx = y sin x 1-

A:

Q: 11. Find the limit using algebraic techniques. The limit of f(x) = -4 O- 0 O=¹ x+4 2x²+5x-12 as x…

A:

Q: 10.) Solve. Write the exact solution in terms of logarithms. el-3x = 4

A: This question can be solved using the concept of natural logarithm.

Q: In this question, you will solve an integral problem using the method of substitution. (a) Make the…

A: A detailed solution is given below

Q: {CLO-1} Find the values of a and b such that the following function is continuous everywhere. ax²-a…

A:

Q: 17. What is the amplitude of the graph y = -4sin (x - 2)? The amplitude is. units. 04 02 O 2T O K|N…

A: For the equation  y=A sinBx+C+D   A-  Amplitude   B- Frequency   C- Horizontal shift   D-  Vertical…

Q: Q: find the cartesian equation of the plane Containing the point p(2.1.1) and parallel to the plane…

A:

Q: 7x Find the linearization L(x,y) of the function f(x,y) = e cos (9y) at the points (0,0) and 0, ¹2…

A:

Q: Given R(t) = 4 cos ti + (1+ 3cost)j +5sintk. Find the arc length of the portion of R(T) from t=0 to…

A:

Q: Find the area of the shaded region. 49- y=49-x² 35- 21- 7- اتنا -17-1 -21- -35- -49- F3 5 th Fo Q Q…

A:

Q: f f(x)=- X+1 2x+1 1 = (2x + 1)²* 1 (2x + 1)² O 3x+1 (2x+1)²* 3x+1 O (2x + 1)² then f'(x) =

A: Topic: derivatives

Q: A piece of cardboard measuring 8 inches by 14 inches is formed into an open-top box by cutting…

A: Question- A piece of cardboard measuring 8 inches by 14 inches is formed into an open-top box by…

Q: {CLO-2} Find all vertical asymptotes of f(x). 4x f(x) = 4-x² Determine whether f(x)→∞ or f(x)→→∞ on…

A: Let's find given function asymptotes.

Q: Find the interval of convergence of the series xn Σ n8" n=1

A:

Q: (c) 1 e¹/x x² dx

A:

Q: 12. What is the amplitude of the graph below? y 4 0 8+ 7+ 6+ 5+ 4+ 3++ -1- -3+ -4+ -5- -6+ -7+ -8+…

A:

Q: 3. Use the limit definition of the derivative to find the derivative of the function. a) f(x) = 2x²…

A: Given query is to find the derivative using definitely.

Q: Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e5xy = sin…

A: Given query is to find the derivative of the expression.

Q: If the population of a city is 155,000. If the population declines continuously by 5% per year, what…

A: Given query is to find the attached population after 15 years.

Q: A company has a security system that uses digits from 1 to 6. a) How many 3-digit security codes are…

A:

Q: nd the derivative of the function at Po in the direction of A. f(x,y,z) = 5 ex cos (yz), Po(0,0,0),…

A: Given query is to find direction derivative at given point.

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 3 ex cos (yz),…

A:

Q: (CLO-3) Find the area of the largest rectangle that can be inscribed in the region enclosed by the…

A: solution:-y=x2-2y=-x2+2let two value of x is -t & t , because the graph is symmetrical about…

Q: 2. Error Analysis. Please complete the following parts in sequential order. a. Solve 2 log4(x-3) +…

A: The given problem is solved below in detail.

Q: Find x' for x(1) defined implicitly byx+x+1-9=0 and then evaluate x' at the point (-2,1). x-2.1)…

A:

Q: 3x + 9 Consider the function f(x): For this function there are two important intervals: (-∞, A) and…

A:

Q: Given R(t) = 4 costi + (1+3cost)j +5sintk. Find || R'(t)||. 5 O 4 O 2 O none of the above

A:

Q: 11.) Solve using matrices and Gaussian elimination: x+y+z= 9 -x-3y + 2z = 10 2x + z = 9

A: Please see the below picture for detailed solution.

Q: 5x² Find all critical points of the function f(x) = 7x²–2x+6* (Use symbolic notation and fractions…

A: For critical points , f'(x) =0.

Q: Use Integration by Parts (IBP) to evaluate the following integral. ² ln(r) + ³ + C 2² In(z)-2³ +C…

A: integration

Q: 2. a) Write sin(3-1) in the form of a + bi. b) Find all the values of (3)-in

A: Concept: Simplifying expressions: Expressions are mathematical statements with at least two terms…

Q: 3 − 4 + 16 - 64 + ...

A:

Q: 10. Find the limit using any technique. The limit of f(x) = 2x² - 3 as x approaches -3. 15 21 limit…

A: To find limit of f(x)