2. Describe the following functions as exponential, quadratic, or linear, or none of them. (4K) a) у х b) f x 2 x' x' c) y 10 x (x 2) 1 d) y 5.2

Q: Consider the following function. f(x) = -x2 - 14x – 2 Find its average rate of change over the…

A: We have  fx=-x2-14x-2 Find the average rate of change of function fx over an interval a, b=-7, 1 is…

Q: Differentiate the following function. y = 5 ex – 2x dx II

A:

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: dP dt т 1- kP 1- M

A:

Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

A:

Q: Is the function a. EVEN h ODD f(x) 1, -π<x<0 1, 0≤x<T

A:

Q: Evaluate the function f(x) = log,x at x = 27 without using a calculator. %3D

A: Given that

Q: Use the Power Rule to compute the derivative.

A:

Q: h) f(x) = e4sin(5z+2)

A:

Q: Consider the following function. f(x) = -x2 - 14x – 2 Find its average rate of change over the…

A: The formula for average rate of change of a function fx over a interval a,b is given as, Average…

Q: Find the linearization of the function F(X) =sqrt (x+3) at a= 1 and use it to approximate the…

A: Therefore linearization at a = 1 is,

Q: Differentiate the following function with respect to X. eX + 3Y =1

A:

Q: Which among the following functions has the derivative of de = (9z - 452 + 272) ( - 2) + (= - 2)*…

A:

Q: Consider the following function. 5x, f(x) = XS1 %3D 5x2, x > 1 Find the derivative from the left at…

A: The derivative from the left side of  x=1 is…

Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

A:

Q: 2. Differentiate the following function: y = Jo tan 2x Hs dt. 1+t3

A:

Q: Let f(x)=xlnx+x. If f'(x)=0, solve for x. Round your answer to 4 decimal places.

A: So,  Given        fx = x lnx +x       f'x = ln x + xx+                = ln x +1  + 1…

Q: 4. y = sech? In x

A: As per bartleby guidelines, for more than one question, only 1st one is to be answered. Please…

Q: Use the first principles definition to determine the derivative of the following quadratic function:…

A:

Q: 2. g'(x) where g(x)= x² +7x-5 %3D

A: ddxxn = n·xn - 1, and ddxC =0

Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

A:

Q: Consider the following function. f(x) = V36 – x² Find the derivative from the left at x = 6. If it…

A: using the first derivative definition of limit

Q: Find a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

A:

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: C. Is the function define by g(x) = x² – sin x + 5 continuous at x = n?

A:

Q: 7. Order the following functions from slowest growing to fastest growing as x→∞. a. e b. x* c.…

A:

Q: For what value of the constant c is the function f continuous on (-, 0)? S cx2 + 5x x3 – cx if x 4

A:

Q: 1. 3y4 + 2xy = 4

A:

Q: 32. Differentiate the following function with respect to y. e + 3º = 1

A: This is a simple differentiation problem

Q: Give the linear approximation of f(x) = x sin(nx2) at x = 2. Use this to estimate f(1.98)

A:

Q: Aen vity # 2 BLs auss ME! t) flx):1 Xスー 2.

A:

Q: Suppose h(x) =log,(3x+1). What is the correct result Зх + %3D of the derivative of h with respect to…

A:

Q: 1 4. Use the definition of the derivative to compute f'(x) given f(x) = 2x 3

A: Given,          The function is fx=12x-3 .

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

A:

Q: 1. f'(5) where f(x) = 2х-3

A:

Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: 2. Use the definition of the derivative of a function at a number to calculate f'(8) where f(x) is…

A:

Q: Find a formula for n.th order derivative of the given functions. 1 b) f(x) = VT 1 a) f(x) = c) f(x)…

A:

Q: Let be the square root function defined by 1 z² = √√√|z|e 2 Show that this function is discontinuous…

A: A complex number is an element of a number system that contains the real numbers and a specific…

Q: If f(2) = 14, f' is continuous, and f'(t)dt = 23, what is the value of f(5)=? %3D

A: Given :

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If 22 + y = 20, and -1 when x = 2 and y…

A: x2 + y2 = 20 Differentiate with respect to t 2x dx/dt + 2y dy/dt = 0 In this equation we put x = 2,…

Q: - Integrate the following function: -3 2x+3 dx y = Jo x²+3x-5

A: The given integral is: y=∫032x+3x2+3x-5dx To evaluate this integral, consider x2+3x-5=t   .....(1)…

Q: If f(2) = 13, f' is continuous, and | f'(t) dt = 27, f(6)? what is the value of Answer:

A:

Q: Differentiate the following functions: 4. y = In (sec 2x + tan 2x)

A:

Q: Differentiate the following functions with respect to x : y = 4x2 +x° – 4x6 1 5 1 y = x3 +-x2 – 4In…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Consider the following function. f(x) = -x2 - 10x – 9 Find its average rate of change over the…

A: