Let f(x) = V30 – x and g(x) = x? – x. Then the domain of fogis equal to a, b] for a = and b =

Q: The domain of the function ,y) = In[x* +y² – 1) is:?

A:

Q: 2y)j + x the point

A:

Q: g(x) = V4t + 5dt. Find g'(2). Let 3-x

A: We have given that  gx = ∫3-xx24t+5dt We have to find g'2 for that we have to use Leibniz integral…

Q: Evaluate the following functions. 1. Iff(x) = x? - 2x +7, find a) f(0), b) f(2y+1). 2. If F(y) = vty…

A: Given:1. fx=x2-2x+72. Fy=yy-32

Q: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: V1-x² 2 dx

A:

Q: find functions f and g so that f ∘ g = H.

A: given: Hx=1-x2 we have to find the functions f and g so that f ∘ g = H.

Q: For the function h(x,y) = 6x + 7y xy-5 7 əh find and ?x əh dy

A:

Q: The domain of the function f(x,y)= V1-x²-y² +In(x²+y² – 1) is empty Select one: O True O False

A: we have to find the domain for f(x)

Q: _1. Differentiate the following w.r.to x (i) V(x? + 1)3 .3,-2x (ii) + In (3x + 1)

A: Using derivative ,

Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

A:

Q: 2.,3 2) Find fx and fy if f(x, y) = 2x²y³ – 3xy² + 2x² + 3y² + 1

A:

Q: Let f(x.y) = In ( x2 + y ). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. 6 O b.3 O. 7 O d. 8…

A:

Q: What is the domain for f (æ) = Væ – 3.

A: Given fx=x-3

Q: Which graph corresponds to the function given? h(x) = {x², x 1

A: Here we have to draw the graph of the function.

Q: Show that A (B × ℃) is not equal to B · (À × ℃)

A:

Q: 5. Assume that V × F = V × G. What is the most general relationship between F and G ?

A: ∇ x F = ∇x G => ∇ x (F - G) = 0

Q: Is the cobb-douglas function strictly concave when a1 +a2 <1 when

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

Q: Find all functions from X = {a,b} to Y = {p,r,t}.

A: Given :- To find all functions from X = a,b to Y= p,r,t.

Q: P=S/(S+F) Express S in terms of F and P

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: Let P(A) = 0.4 "and " P(AU B) = 0.6. For what value of P(B) are A "and " B are independent?

A:

Q: Compute f(s), where f(z) = e and 8

A: The given function is  and

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.