25-28 - Logarithmic Form Write the equation in logarithmic form. 25. 2° = 64 26. 49-12 = %3D 27. 10 = 74 28. e* = m

Q: Find the limit, if it exists.

A: It is given that, limx→∞xx2+1We have to find the limit,if it exists.  

Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line. (I...

A: Horizontal tangent means slope of a line is equals to 0 Given, y=x+5ex

Q: Determine whether each integral is convergent ordivergent. Evaluate those that are convergent.   ∫-∞...

A: Given, ∫-∞∞xe-x2dx

Q: Use the two steps for solving a linear programming problem given to solve:You are about to take a te...

A: Let x represents the number of computation problem. and y represents the number of word problems. so...

Q: Change the order of integration of the integral ∫10 ∫y0 ƒ(x, y) dx dy.

A: Change the order of integration:Change the order of integration means to change the pattern of integ...

Q: If $2500 is invested at an interest rate of 2.5% per year, compounded daily, find the value of the i...

A: Given, The initial amount, P=$2500 Rate of interest,r=2.5% Compounded daily,n=365

Q: Find the area inside the circle r = 2cosθ and outside the unit circle r = 1.

A: Given that: r=2cosθ  and   r=1 To calculate the intersection points, 1=2cosθcosθ=12θ=π3   and   -π3 ...

Q: Use the Divergence Test, the Integral Test, or the p-series test to determine whether the following ...

A:

Q: Write the definition of the definite integral of a function from a to b. (b) What is the geometric i...

A: Definition of definite integral Geometric interpretation of f(x) for f(x)>0 

Q: Find the general solution to the given differential equation. (Use C for the constant of integration...

A: Solution:- The given differential equation is  e8x(y+1)dx+e4xy dy=0  

Q: 2. Consider the graph of the functions f, and g (below). yA 1 1 a) Which is larger, f(6) or g(6)? b)...

A: Given that, The graphs of function f and g as follows:  

Q: Graph the polynomial function: f(x) = 2x2(x - 1)3(x + 2)

A: The polynomial function f (x) = 2x2 ( x - 1)3( x+ 2).  

Q: Partial derivatives Find the first partial derivatives of the following functions. s(y, z) = z2 tan ...

A: Consider the provided function, Sy,z=z2tanyz Find the first partial derivatives. So, we find the exp...

Q: My graph of f(x) = 3 . 2x shows that the horizontal asymptote for f is x = 3.Determine whether the s...

A: Consider the given function as fx=3·2x

Q: Use vectors to find the point that lies two-thirds of the way from P to Q.      P(1, 2, 5),    Q(6, ...

A: Solution:-  Given that  point P(1,2,5) and point Q=(6,8,2) let M(x,y,z) be a point that lies two-thi...

Q: Solve the equation 3x3 + 7x2 - 22x - 8 = 0 given that - (1/3) is a root.

A: Given, 3x3+7x2−22x−8=0 and x=−13is a root. Formula: If x=a is a root of equation, then x−a is a fact...

Q: Find the general solution of the differential equation y′ = 1/ x√(4x2 − 9)

A: To find the general solution of the differential equation y'=1x4x2-9

Q: Evaluate the integral ∫tan7 x/2 sec2 x/2 dx

A: We have to evaluate the integral: ∫tan7 x2 sec2 x2 dx Here we will use substitution method since der...

Q: Jx?, x is rational 1o, x is irrational. Let f(x) Show that f is differentiable at x = 0.

A: Given, We know that, fx=px     , x is rationalqx     , x is irrational  is differentiable only at r...

Q: find Ly for the given differential operator if (a) y(x) = 2e3x, (b) y(x) = 3lnx, (c) y(x) = 2e3x +3ln...

A: Given: L=D3-D+4 (a) y(x)=2e3x Ly=D3-D+42e3x    =54e3x-6e3x+8e3x    =54e3x+2e3x

Q: Plot the point given in polar coordinates. (-1,) 8 27 Find three additional polar representations of...

A: We have to plot the point -7,2π3 in the polar coordinates. Also, find the three additional polar rep...

Q: Solve the homogeneous equations. First put theequation in the form of a homogeneous equation. (x2 + ...

A: Given:           (x2 +y2)dx−xy dy=0   ​   ⇒ (x2 +y2)dx=xy dy⇒dydx​= x2 +y2xy  ............1 Let y=vx...

Q: Choose a convenient order When converted to an iterated integral, the following double integrals are...

A: Consider the given double integral, ∬RycosxydA  where R=x,y: 0≤x≤1, 0≤y≤π3 now, it is easier to take...

Q: Find an equation of the line that passes through the point and has the indicated slope. Then sketch ...

A: Given, (-8,1) Since the line has an undefined slope. This informs us that it is a vertical line para...

Q: Use Integration by Parts with u = x and v' = bx.

A: Given, u=x  &  v'=bx

Q: The following sequence, defined by a recurrence relation, are monotonic and bounded, and therefore c...

A: Solution:- The given sequence is  an+1=(2+an) ; a0=3 a. Examine the first three terms of the sequenc...

Q: Solve : (2x + 3)(x + 4) = 1

A: It is given that,(2x + 3)(x + 4) = 1 We have to solve it.  

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Find limx→ -1 ƒ(x) algebraically.

A: Given f(x)=(x2-1)/(|x|-1). We need to find limx→ -1 ƒ(x).  

Q: Use 105° = 135° - 30° to find the exact value of sin 105°.

A:

Q: Express the given interval in set-builder notation and graph the interval on a number line: (- ∞, 3....

A: Given information: The interval is (- ∞, 3.5]. Set-builder notation: {x:x∈ℝ,x≤3.5}      

Q: Find d2y/dx2 implicitly in terms of x and y 7xy + sin x = 2

A:

Q: Are the addition formulas and double-angle formulas similar?

A: Solution:-  The question is  Are the addition formulas and double-angle formulas similar?  

Q: Calculate the area bounded by y=x³, x=0 and y=3.

A:

Q: Write a rational function with vertical asymptotes at x = 6 and x = −2, and with a zero at x = 3.

A: Given vertical asymptotes of a rational function are at x=6 and x=-2. Also zero is at x=3. We know t...

Q: Integer

A:

Q: f(x) = 2x3 + 6x2 + 5x + 2 a. List all possible rational zeros.b. Use synthetic division to test the ...

A: a) By the Rational Zero Theorem, the possible rational zeros of a polynomial function are determined...

Q: Insert either < or > in the blank area between the numbers to make the statement true, √2 ….. ...

A:

Q: A ball is thrown upward to a height of h0 meters. After each bounce, the ball rebounds to a fraction...

A: Consider the following curves: x=cost+tsint  ,  y=sint-tcost Use the statement of derivative for Par...

Q: (a) If g(x) = 2x +1 and h(x) =4x2 +4x  +7 , find afunction f such that f ° g =h . (Think about what ...

A: a) Given that, gx=2x+1hx=4x2+4x+7