2. Differentiate the following, then simplify. e2x-ex a) y = ex b) y = c) Find the inputs that generate a horizontal tangent line. x² y = x-1 3 -2x²

Q: The graphs of the functions f and g are shown in the figure. y -1 Let u(x) = f(x)g(x) and v(x): =…

A: Given: Let  and To Find:

Q: Solve the separable equation dy/dx + 4x2y4 = 0, with initial value y(0) = 1.

A: Take integration on both sides.

Q: Find all solutions of the following equation in the interval [0, 2π).    sin^3x=sinx

A:

Q: Use the method for solving equations of the form following differential equation. dy dx 19x + y - 19…

A:

Q: Determine whether the equation is exact. If it is, then solve it. ( 7 ) ax - (2x - 3 dx 2y 4x 2 dy =…

A:

Q: Use Simpson's Rule and all the data in the following table to estimate the value of the integral X y…

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y)=xy-3y², Po(-8,-10), A= -2i-j…

A:

Q: The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and…

A: This is question of calculusHere rate of change is given We have to find displacement.Further…

Q: Find F as a function of x and evaluate it at x = 0, x = π/6, and x = π/2. X force 0 F(x) F(0) F(T)…

A:

Q: Simplify the expression algebraically. ​   ​sin(9x-9y)sin(9x-9y)

A:

Q: Find implicitly: dx In(xy²z) + x²z² + 2xy³ = 1

A: The given equation is

Q: Show that (csc(x)) = −csc(x) cot(x). dx (csc(x)) dx = = d dx = 1 sin²(x) 1 sin(x) = -csc(x) cot(x)…

A:

Q: 2. Find d [ex (x4 * (x² +1)x] dx ¹]. X

A:

Q: The sum of the first 100 terms of the arithmetic series 3 + 1 + (-1) + (-3) + ... is

A:

Q: (2xy + x² + x4) dx − (1 + x²) dy = 0

A:

Q: Let f(x)= 2x1 3x + 2 a. Find the domain of the function. b. Find the y-intercepts, if any. c. Find…

A: The given function .The aim is to find the vertical and horizontal asymptotes and sketch the graph…

Q: Find f. f(x) = f"(x) = cos(x), f(0) = 9, f'(0): = = 8, f "(0) = 6

A: Given,  f'''(x)=cosx, f(0)=9, f'(0)=8, f''(0)=6

Q: Let f(x) = 2 cos z + 7 tan x f'(x) f = 5 п =

A: Given, we know,

Q: Problem 4: Let f(x)= 42-4 1²-1-6 a. Find the domain of the function. b. Find the y-intercepts, if…

A: The given function is,To find the domain, take the denominator=0So the domain is,

Q: 16. Write a linear function f that has the indicated values. Sketch the graph of f. f(0) =-3, f(2)=…

A: f(0)=-3,  f(2)=-4So, points are (0,-3)& (2,-4)

Q: Find a general solution to the differential equation. 1 1 y" +6y=4 tan 6t - e²t 2t

A:

Q: 13. Letf(x)= 3x 25-x Find each function value. a. f(0) b. f(1) c. f(5) d. f(-5) e. f(-x) a. Find…

A: The given function is; f(x)=3x/sqrt(25-x2)According to Bartleby guidelines we solve only three parts…

Q: Write the expression as a logarithm of a single quantity. 7 =/=/= (In(x² + 4) - In(x + 3) - In(x −…

A: This is question of calculus Here logerithmic function is given We have to make it in one term…

Q: The function P(x) = − 2.25x² + 1775x – 9500 gives the profit when a units of a certain product are…

A: a=According to Bartleby's guide line we only do first three parts of multiple part questions.Given,

Q: Find f"(x) if f(x) = = 25 x-4 70 (x − 4)²

A: We need to calculate f''(x) for the given function f(x). This can be evaluated as follows:

Q: derivative y = 3 2(4x-1)

A:

Q: Determine whether the equation is exact. If it is, then solve it. (cos xsin y-2x)dx + ( sin x cosy -…

A:

Q: 23 f(t) = (t, t Between = 0 and = 1, the point traverses certain path. The length of that path is

A:

Q: Verify that the function y(x) = cos(3x) is a solution to the differential equation y′′+ 9y= 0

A: The given solution is,Take derivative.Take the second derivative.

Q: 59. y = e sinx

A:

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

A: Given Definite Integral

Q: Answer these following For B try by first using properties of integrals A Sh(x)dx = 214. BS₁,…

A:

Q: 2. Find the first order and second order partial derivatives of f(x,y) =x. Make sure to show your…

A: The given function is Note:-Since you asked parts 6 and 7 for the given problem but here in given…

Q: Use the quotient rule to differentiate the function f(x) = f'(x) = x-3 -2x+2

A:

Q: (1) Evaluate solution= Hint: Express cos a in terms of sin a. Then use the substitution usinx. Back…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x.…

A:

Q: (f) The equations of the asymptotes (in increasing order). (c) I (a) 2 (d) N (f)x= y = (b) -2 (e) N…

A:

Q: A fence is to be built to enclose a rectangular area of 310 square feet. The fence along three sides…

A: Let x be the length of the rectangle and y be the width of the rectangle.The area of the rectangle…

Q: How to formula asin BØ + bcos BO а √a²+ b² cos (BO-C) Where C= arctan (a/b) C = arc tan (a/b), a>0…

A:

Q: 5. Evaluate the following integrals. 3 1 3 (a) Sò Sở 5g®ex® dady; 35/2 3 (b) 2/5 sin(y) dydz. So…

A: To evaluate the following integral.

Q: Find Əw Əv Əw Əv y when u = 0, v = 0 if w = x² + x = 2u - 4v + 1, y = 6u+v-2. X lu = 0, v = 0 =…

A: To find:

Q: Using either the triangle inequality or the reverse triangle inequality, prove the following: ii)…

A: To prove the statement |2x−3|≤5 when |x−3|≤1, using the triangle inequality. The triangle inequality…

Q: Find points. tangent line is horizontal f(x)=4x^2-2x+3

A:

Q: Evaluate the following expression. (x ≠ πn, where n is a whole number)   3/sinx - 3/cscx

A:

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A:

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A:

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

A:

Q: Find a formula for the derivative of the function g(x)=3x2-1 using difference quotients:…

A: g(x)=3x2-1

Q: 2 Find the area of the region enclosed by the graphs of f(x) = x² + 2and g(x) = 2x + 5.

A:

Q: dw For the given functions, (a) express as a function of t, both by using the Chain Rule and by…

A: