f(x) = 4 – x², g(x) = /x + 1 (a) lim f(x) (b) lim g(x) | (c) lim g(f(x)) х 1 1 x 3

Q: 2. Complex Operations Write the following complex numbers in the form a + bi. (b) (2+ 3i)(1 + i) 2+i...

A: Given: 2+3i4-i, 2+3i1+i, 11+i for converting given expression in a+bi  form, we apply given operatio...

Q: Integration Evaluate the following integrals.

A: Given: I=∫81dxx3-9x2 for evaluating given integral, we first simplify it then integrate is so, ∫81dx...

Q: Find f, f'(x) = 20x3 + (1)/(x), x > 0, f(1) = -3 f(x) =

A: Givenf'x = 20x3 + 1x, x > 0, f1 = −3

Q: Among all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What ...

A: we know that product of two numbers will be maximum if both number are equal so, assuming both numbe...

Q: Use the product rule to simplify the expressions .Assume that variablesrepresent nonnegative real nu...

A: To compute:                      27  

Q: Fill in the blank/s: A sequence of equal payments made at equal time periods is called a/an ________...

A: Given data: A=P1+rnnt-1rn A sequence of equal payments made at equal time period is called an annuit...

Q: Use a system of linear equations with two variables and two equations to solve. 246 students enrolle...

A:

Q: Find an equation for the tangent to the curve at the given point. Then sketch the curve and the tang...

A: Consider the provided equation, y=-12x3 Find an equation for the tangent to the curve at the given p...

Q: use logarithmic differentiation to find thederivative of y with respect to the appropriate variable

A: the given expression is: y=2x2+1cos2x we have to use the logarithmic differentiation to find the der...

Q: Solve the logarithmic equation 3 log2(x - 1) = 5 - log2 4. Be sure to reject any value of x that is ...

A: Given equation, 3log2x-1=5-log24

Q: Use a graphing utility to sketch the intersecting graphs of the equations and show that they are ort...

A: Given : x 3 = 3 ( y − 1 ) x (3 y − 29) = 3   To determine :  Using a graphing utility to sketch the ...

Q: Let θ be an angle in standard position. Name the quadrant in which θ lies. tanθ> 0 and cos θ <...

A: tan θ>0 and cos θ<0

Q: c) Sa* sin*x dx

A: To evaluate : The integral  ∫π43π4 sin4 x dx . 

Q: 4.8 please show me all steps

A:

Q: The larger circle in the figure is the graph of r = 1. Find the polar equation of the smaller circle...

A:                           From Pythagoras Theorem AB⇒r=r12          1=r12          r1=12 Let radius ...

Q: The equation y = mx + b shows that no line can have a y-intercept that is numerically equal to its s...

A: Given: The statement "the equation y=mx+b shows that no line can have a y-intercept that is numerica...

Q: Sketch a graph of a function ƒ, where ƒ(x) > 0 and ƒ′(x) < 0for all x in (0, 2).

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Solve the equation on the interval 0s0<2n. - sin 20+ cos 20 = sin 0+ 1 Select the correct choice bel...

A: Given, -sin2θ+cos2θ=sinθ+1

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

A:

Q: Find a positive number a such that the sum of 25x and is as small as possible. Does this problem req...

A:

Q: Find an equation of the tangent line to the curve atthe given point.y =sqrt ( 1 + x 3 ),            ...

A: Given, y=1+x3 , (2,3)

Q: Solve the triangle a = 66, b = 25, c = 45. Round lengths of sides to the nearest tenth and angle mea...

A: Solution:- It is given that   a=66b=25c=45

Q: The value V of a machine t years after it is purchased is inversely proportional to the square root ...

A: Given, The value V of a machine t years after it is purchased is inversely proportional to the squar...

Q: Find the product. (x + 8)(x + 5)

A: Given : (x + 8)(x + 5)

Q: Solve the equation on the interval 0s0<2R 4 sin 0+5 =7 What are the solutions in the interval 0s0< 2...

A:

Q: The components of v = 240i + 300j represent the respective number of gallons of regular and premium ...

A: Vector: The components of v = 240i + 300j represent the respective number of gallons of regular and ...

Q: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to &lt...

Q: Please show the steps  thank you

A: Given at=24t+12s0=1 and v0=7

Q: Differentiate the function.  v = t2 - 1 / fourt root of t3

A: Given function is v=t2-1t34. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating ...

Q: Find ∫sin23x cos 3x dx

A: Given:                  ∫sin2(3x) cos(3x)dx   Integrating:                    Let's apply the u-subs...

Q: Use the information to evaluate the limits.

A:

Q: Solve the polynomial inequality x2 + 5x + 4&gt; 0 and graph the solution set on a real number line. ...

A: Given, x2+5x+4&gt;0⇒x2+252x+522-52+4&gt;0⇒x+522-254+4&gt;0⇒x+522-94&gt;0⇒x+522&gt;94⇒x+52&gt;±32⇒x&g...

Q: Compute the limit:lim (1+3x)^(-5/x)x→0

A: We have to evaluate the given limit.

Q: The function C(t) = 20 + 0.40 (t - 60) describes the monthly cost, C(t), in dollars, for a cellphone...

A: Solution:-  The monthly cost =C(t)=20+0.40(t-60) where C(t) in dollar, for a cellphone plan for t ca...

Q: The function f(x) = (6.5x2 - 20.4x + 234)/(x2 + 36), models the pH level, f(x), of the human mouth x...

A: To Determine: a) Use the graph to obtain a reasonable estimate, to the nearest tenth, of the pH leve...

Q: Use integration by parts to prove the formula. ( assume that n is a positive integer.)

A: To prove : ∫ xn eax dx  = xn eaxa - na ∫ xn-1 eax dx

Q: please show all the steps and work. Thank you

A:

Q: Perform the indicated operations: 1 /( xn - 1) - 1/ (xn + 1) - 1/ (x2n - 1) ?

A: Given,            1xn-1-1xn+1-1x2n-1

Q: Establish the identity. (5-) - sin cos 0 %3D

A: Given,          sinπ2-θ=cosθWe know that,           sinA-B=sinAcosB-cosAsinB

Q: Radioactive decay The mass of radioactive material in a sample has decreased by 30% since the decay ...

A: Let C(t) be the mass of radioactive material in a sample of t years after the initial mass C0. Then,...

Q: Consider the following five functions.• a(x) = x − 2 • b(x) = |x| • c(x) = x + 2 • d(x) = −x • e(x) ...

A: Given, ax = x-2bx = xcx = x+2dx = -xex = x+4   fx=e∘d∘c∘b∘ax   f(x) is the composition of the five f...

Q: Fill in the blank/s: If the occurrence of one event has no effect on theprobability of another event...

A:  If the occurrence of one event has no effect on the probability of another event, the events are sa...

Q: In Exercises 23-38, either use the formula for the sum of a geometric seriesto find the sum, or stat...

A: Given series:                       ∑n=-4∞ -49n              

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.