For y = f(x) = 7x², find f(x₁+AX)-f(x₁) Ax || f(x₁ +Ax) -f(x₁) Ax given x₁ = 5 and Ax=2.

Q: Seperate the variable and solve the equation 2y (dy/dx) + 2x = 0. Use the initial condition x = 0;…

A: The given equation .The aim is to find the solution with the initial value .

Q: =D x. 19

A:

Q: Find the measures of the sides and angles. Round angle measures to the nearest tenth of a degree.…

A:

Q: The answers for N[T(t)], t=2hr, and t=5hr are wrong.

A: Given:To find: (a) To compute .(b) To find the number of bacteria present when .Note: After seeing…

Q: The graph of the derivative g' has exactly two roots. Complete parts a through c. OA. The function…

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 2t²1 - 4tj + (a) r(t) (b) r"(t) (c)…

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 12 + 2x -…

A:

Q: Use implicit differentiation to find dy/dx of tan(x+y)=2y

A:

Q: Step 3 Write the two binomial factors so that the first term of each factor is x and the second…

A: To write the complete factorization of

Q: he graph of the derivative g' has exactly two roots. Complete parts a through c. OB. There are no…

A:

Q: Recall that a sequence is a list of numbers while a series is a summation of numbers. 1. Let an = n…

A:

Q: Consider the function INTERMEDIATE WORK Using calculus give a sketch of y. Make sure you include the…

A: The given function equation is

Q: 3) Prove the following statement using the Intermediate Value Theorem (IVT): 2+3* = 4* has a…

A: Question No. (3):To prove the following statement using the Intermediate Value Theorem (IVT):  has a…

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

A: The given graph

Q: (1) (2 cos y + 4x²)dx = xsin ydy

A: given differential equation

Q: To test this series for convergence ∞ n=1 n n6 + 7 You could use the Limit Comparison Test,…

A:

Q: (a) Consider the curve y = x - 3x7. d.x (b) This function is not differentiable when = (c) (Give…

A:

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A:

Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

A:

Q: 2. Determine whether the series n Σ» (-1) (3) converges or diverges. If it converges, find the sum.

A: The given series is

Q: Evaluate the indefinite integral. 0+ +C 54 sin x COS X dx

A:

Q: Compute the average rate of change of the function on the given interval. g(x) = x³ x on [4, 5] -

A:

Q: What values of a and b make the function f continuous everywhere? x² 4 a = f(x) = and b = - " X 2…

A:

Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

A:

Q: Sx ³√x²+4 3 S

A:

Q: Find the derivative  a. y= ln(cos^2x) b. y= e^cosx+e^-x

A:

Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to write the given function as a composition of two functions.

Q: 1. Solve dy_3-x-y x + y €1 dx 11

A:

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A:

Q: Find the inverse matrix where A = 1 -1 2 -3 -3 1 2 -3 -3

A:

Q: Evaluate the following integral. A sketch is helpful. R 3 15x² dA; where R is bounded by y = 0, y =…

A: To find:- Where R is bounded by

Q: Consider the following curve. ² = sin(20)

A: r2=sin⁡(2θ)

Q: Consider the function f(x) = 2x³ – 2x on the interval [-5, 5]. (a) The slope of the secant line…

A:

Q: An employee's monthly productivity M, in number of units produced, is found to be a function of the…

A: An employee's monthly productivity M, in number of units produced, is found to be  a function of…

Q: differentiate y(theta) = e^cot theta

A: given function

Q: Find the general solution of the first-order linear equation dy dx + 2y = e²x

A:

Q: Let f (x) = - x² – 3. Find and simplify ƒ' (x) and ƒ" (x). x5 f" f'(x) = A = -3 B C = || f" (x) D E…

A: Given Function f( x ) as follows

Q: Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by…

A: Given that, where R is the region bounded by the graphs of                  Using the change of…

Q: 4. Let f(x, y) = (a) (1,-1). Find the slop of the surface z = f(x, y) in the x-direction at the…

A: given function

Q: TO Find the length of the curve y = In (2 sec x) for 0 ≤x≤ xs 6 The arc length of the curve is (Type…

A:

Q: Use spherical coordinates. Evaluate JJJ y²z² dv, where E lies above the cone 4 = 1/3 and below the…

A: G

Q: Find a Cartesian equation for the curve. r = 5 sec (0) 2π X

A:

Q: Find the area of the shaded region. y 3 2 1 (1, 1) 2 y = ³x y || 4 1 X 6 X = 8 CO 8 X

A: Given equations of the curve

Q: Find all critical numbers c of f(t) = 3t²/³ +t5/³.

A: f(t)=3t2/3+t5/3

Q: If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) X

A: The Quotient Rule:Use the common derivatives:

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A:

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 11.…

A:

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve .The aim is to find the slope of the tangent line to the polar curve at the…

Q: Show that the functions are linearly dependent on the real number line: y1 = 17; y2 = 3cos2x; y3 =…

A: The given functions are  and .The objective is to show that the functions are linearly dependent on…

Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ"(x)(x − b)dx - a

A: