Show that (1+:)'→e. as x → o, → e. HINT: Since the logarithm function has derivative 1 at x = 1, %3D In (1 + h) – In 1 In (1 + h) → 1. - as h → 0, h

Q: Q4 Solve the equation sin 40 = cos 30 within the range -180 <0S180.

A: Basic calculus problem

Q: An airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider 0 and...

A: Given data H=5miles Speed =336 miles per hour We have to determine angle  

Q: 7x Use – ∞ and co when appropriate. Find the limits in a), b), and c) below for the function f(x) = ...

A:

Q: Find all the values of a such that the given series would converge. (7x)" n5 n=1 The series is conve...

A:

Q: For the function f(x) given below, evaluate lim f(z) and lim f(r). f(z) = 6r 673

A:

Q: In Exercises 47–54, find the reference angle 0'. Sketch 0 in standard position and label 0'. 48. 0 =...

A: Given that: 48. θ=309°50. θ=-215°

Q: Bray?) da (y ) (x+zy+3)da - (2x-4+1)dy =0

A:

Q: 6. f(x) = V7x + 6; f'(3)

A:

Q: Differential Operator General Solution DN AxN-1 + BxN-2 +..+C (D - a)N AxN-leax + BxN-2eax + ... (D?...

A: differential equations

Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). I-00 f(x) = -3x* Provide...

A: topic - limits

Q: дт ду д dy at az az & as Calculate by first finding & and using the chain rule. at as' as' at

A: Follow the procedure given below.

Q: P(#) Question 4: When working with rational functions of the form f (x) = and the function does inde...

A:

Q: Determine whether the statement is true or false. Modify each false statement to make it a true stat...

A: Given that: If a number is divisible by 2 and 3, then the number is divisible by 6.

Q: Verify that f has an inverse function. Then use the function f and the given real number a to find (...

A: f(x)=18x5+5x3; a=-9

Q: Determine the convergence of the following series

A: let ∑an n=1∞ be an seriesconvergence of the series can be detremined the ratio test.iflimn→∞an+1an &...

Q: The temperatue of a town t months after January can be estimated by the function f(t) = – 28 cos( + ...

A: Given that: f(t)=-28cosπt6+41

Q: Select ALL statements true about the function whose graph is shown below. A. The function is defined...

A: The limit of the function at a point 'a' in its domain is the value of the function approaches as it...

Q: 1. Determine the important parts of the conic and sketch their graph. а. у? + 2х — 10у — 31

A: As per our guidelines we are supposed to answer only one question i.e. the question no 1)a). For the...

Q: Use implicit differentiation to find the tan x sec?x 9. y' of sec?x + csc²y = 9 ans. y' = coty csczy...

A: topic - implicit differentiation

Q: 2. An area is bounded by the curve y = 8/(x² + 4), the x-axis, and the lines x + 2 = 0 and x-2 = 0. ...

A: Given, The curve bounded by y =  8/(x2+4) and x axis (y=0) And lines x+2=0 and x-2=0 x= -2 and x=2

Q: t Complete the table of values to evaluate lim t0 sin t f(t) f(t) -1 1 -.5 0.5 -3 0.3 --1 0.01 -.001...

A:

Q: Compute the total area A of the (infinitely many) triangles in the figure, if the height h of each t...

A:

Q: yx+1 y=0, 0. 7 about the ras Siatch the region. Skatch the solid. and a typical disk or washer 10

A: Here, the given region is bounded by the curves: y=x+1, y=0, x=0, x=7

Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ = y...

A:

Q: Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = x2 - 6xy ...

A:

Q: 5. A wooden block is made as shown in the diagram. The ends are right-angled triangles having sides ...

A: Given Total surface area = 7.200 cm2

Q: The temperatue of a town t months after January can be estimated by the function f(t) = – 28 cos( + ...

A: The solution can be seen below.

Q: Let f(x,y) = ln(100 − x^2 − y^2). a. Find the domain of this function. b. Find the boundary of the d...

A: We know domain of log(x) is (0, infinity)

Q: A. Evaluate the following integrals by substitution. 1. Sx(2x? + 3)®dx

A: Put (2x2+3)= t  Differentiating both sides  4x dx= dt    

Q: se at (r, s) = (1,0), where ds Use the Chain Rule to evaluate the partial derivative S(x, y) = In (x...

A: Given:- f(x, y) = ln(xy) , x=3r+5s , y=2r+9s  To find:- By using chain rule to evaluate the partial ...

Q: Given f (x) = {r²+ k_ if-1< x skx – 3 if x<-1 | . Find the value of k such that lim f(x) exists. X--...

A: Topic = Functions

Q: if a 2 Compute the quantities below. Write "DNE" if the limit does not exist or the value is undefin...

A: Given that: f(x)=7x+7     if    x≤27x-8      if   x&gt;2

Q: Given a function whose graph is shown below. 1 0.5 -5 -4 1 2 -0.5사 -1.5 Determine lim f(x). r--1

A: We have the find the limit of f(x) at x = -1 using the graph of f(x).

Q: cos(2x)81-x (x*+1) Given f (x) = Use logarithmic differentiation to find the derivative of the funct...

A: According to question,Given function,fx = cos2x81-x4x2 + 1

Q: (2xy-tany)dx + (x² – xsec*y)dy = 0; y(1) = *

A:

Q: A. Evaluate the given limits. 1. lim 0 X-1

A: Topic = Limits

Q: Given a function whose graph is shown below 6- 5- 4- f(x) -3 -2 |-i 0 1 2 3 4 5 -1 -3 What is f(1)? ...

A: for x=1 there is no corresponding y value , That is there is no close circle for x=1, Therefore f(1)...

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A:

Q: What is the equation (mathematical expression) for a hollow sphere with center at the origin and rad...

A: According to question,Given,Center of hollow sphere =Origin 0,0,0,Radius = 10

Q: Find the derivative of the equation: h(w)=(5/2)(w2+8w+1)(3/2)(2w+8

A:

Q: 1 n = 2

A: Telescoping series are series in which all but the first and last term cancel out.

Q: 55-68, evaluate the sine, cosine, and tar of the angle without using a calculator. 58. 675° 2n 64. 3

A:

Q: If f. g and h are functions defined on the set of real numbers defined by: F(x)= 3x+1, g(x) = 2x -1 ...

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: Given: y=x+1, y=0, x=0, x=7

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: Determine if the given function is a continuous on each of the given intervals. A. f(x) = 3x³ + 4x² ...

A:

Q: *The limit of a function Evaluate the given limits numerically (using table of values) and graphical...

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the equation...

A:

Q: dx 3.

A:

Q: 1) Consider the graph of the function f(x) = 5x -8x a) Find the slope of the secant by sketching a g...

A: