2. Draw a function with the following criteria: lim f(x)=2, f(-5)=-4 X-5 lim f(x)=0, lim f(x)=7,f(3)%3D0 x3*

Q: Evaluate the limit of the function: lim f(x) =- /7 +x -V7

A: topic - limits

Q: Find the indicated limit given that lim f(x) = 5 and lim g(x) = 4. xa lim [2f(x) – 4g(x)]

A:

Q: If f(x)=2-3x². O a. O b. O c. lim h→0 lim h→0 lim 30 From first principles select the correct step.…

A: Given :fx=2-3x2

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

A:

Q: Given the graph of y = f(x), y y = f(x) 1 2 3 -1 -2 lim f(x) = 1 then x→2 OTrue

A: Check value of f(x) at x=2

Q: Given the function f ( x ) = 1 /(x + 3) . Find  lim Δx ⟶ 0 (f ( x + Δx ) − f ( x ))/ Δx

A:

Q: Find the limit. x+y-9 lim Vx+y - 3 (X.y)→ X+y#9

A: To solve the limit

Q: lim V3x² – 6 X-2

A: The given problem is,           limx→23x2-6 Here the function is continuous and defined at x=2, so…

Q: sketch the graph of a function with the given limits.

A: the given limits are:

Q: Determine whether the shown statement makes sense or does not make sense, and explain your…

A: The functions whose graphs can be drawn without lifting the pencil off the paper is a continuous…

Q: Find the indicated limit given that lim f(x) = 5 and lim g(x) = 2. xa lim V3f(x) + 6g(x) xa

A:

Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

A:

Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

Q: Given the graph of y = f(x), y y = f(x) 1 2 3 -1 -2 lim f(x) = 0 then x→1 OTrue O False

A:

Q: Find the limit of the function lim x → − 6 ( 2 x + 12 | x + 6 | )

A: Find the limit

Q: 16. Find the equation of the line tangent to the functionf (x) = 6Vx at x-4. *hint: use lim,a…

A:

Q: ; Be h(x) = - 2x + 1, x + 3 calculate lim h(x) 7,x = 3 x-3

A:

Q: Verify the limits in a given equation below. (2х-4)2 lim X→3 x+1

A:

Q: If you know in advance that lim f (x) exists, can you determine its X+5 value from a plot of ƒ for…

A: Given that limit of f(x) exists at x=5.That means the function f(x) is continuous and differentiable…

Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: 2. Consider the function: + 3 if x 2 %3D 17 if x = 2. %3D Find lim, 2 f(x).

A: Function given is- f(x)=x2+3       if x<2x3-1      if x>217           if x=2  To find…

Q: Find the limit of the function lim x² 3x +2 X-1 X-A

A:

Q: Suppose a state's income tax code states that tax liability is 18% on the first $19,500 of taxable…

A: The tax function,   T(x)=a+0.18xx≤19,500b+0.14x-19,500x>19,500

Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

A:

Q: Use the graph to evaluate the indicated limit. 4. lim f(x) 5. lim f(x) 6. lim f(x) x2 yA (2, 3) 4…

A: limit of function

Q: Find the limit of the function lim x → − 2 ( 2 − | x | 2 + x )

A: Topic:- calculus

Q: Evaluate the given limits numerically (using table of values) and graphically 1. lim2 X-2 x-2 f(x)

A: x 1.9 1.99 1.99 1.999 2.001 2.01 2.11 f(x) 3.9 3.99 3.999 4.001 4.01 4.1 4.11     limx→2x2-4x-2…

Q: Based on the previous item, what is x + 2 lim x→1+ x – 1.

A:

Q: 2x-1 2. lim X-2 \3x+4,

A:

Q: 3. Is lim f(x) always equal to f(c)?

A: Is limx→cfx always equal to fc The given statement is not necessarily true.

Q: Q4) A) Find the following limits (for two only). x+1 1. lim x--1x²-x-2 1-Vx 2. lim x→1 1-x 2x 3. lim…

A:

Q: Using tables of values, estimate   lim 3x

A:

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: lim (In 2x + 5) + 4 X→ー1

A: Solution:limx→-1ln2x+5+4=ln2-1+5+4

Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

A:

Q: et a) f(x) = x 20 lim f(x) = -x, x <0' x→0

A:

Q: Find the value of the positive constant c such that....

A: Given- limx→∞x-cx+cx=14 To find- The value of c. Concept Used- If any limit of the function fxgx in…

Q: Determine the limit at infinity. 4x -6x2 + 3x lim - -x - 2x+6 O A. 4 OB. OC. 0 D. 4.

A: Given limit is Dividing both numerator and denominator by x^3, we get

Q: Q4) A) Find the following limits (for two only). x+1 1. lim x--1 x2-x-2 1-Vx 2. lim x-1 1-x 2x 3.…

A: 1. limx→-1 x+1x2-x-2   is of 00form, So apply L'Hospital rule limx→-1 x+1x2-x-2   =  limx→-1…

Q: lim (-2 xS t x-1)

A: From this limit, we know that when x approaches -infinity then y approaches +infinity. so, on the…

Q: 1. Using the table of values, estimate lim 3x x-2 а. 3 b. 6 с. 2 d. 5 2. Using the table of values,…

A: Given: L1=limx→23x, L2=limx→1x2+4x-3, L3=limx→2-x3+2x2-3, L4=limx→2+x3+2x2-3 We know that for any…

Q: The cost of manufacturing a particular basebal cap is C(x) = 10,000 + 5x, where x is the number of…

A: Given that:

Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

A:

Q: Determine the following limits at infinity. lim x-11 xS-0

A: limx→-∞x-11

Q: show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.

A: We will see that along y=mx2 path limit does not exist which means limit does not exist.

Q: Find the following limits. x²+3x-4 x -16 1. lim 2. lim X-1 X-1 x+2

A: Apply the limit to the given expression and if it results in 0/0 form then take the derivative of…

Q: 6) Find lim f(x). X>T/2

A: Given graph we have to find limx→π2f(x)

Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

A:

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) X→-1

A: A limit tells us the value that a function approaches as that function's inputs get closer and…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.