. Evaluate each expression using the functions (-x, u - 1, -2 sx<0 f(x) = 2 - x, gx): 0sxs 2.

Q: Find a function f and a positive number b such that f(t) dt t6 1+ 6x-3

A: To find a function f and a positive number b

Q: For what value of the constant c is the function f continuous on (-00, 00) ? S cx? + 8x RX) = {-x x3…

A: The given function will be continuous when limx→3+fx=limx→3-fx.

Q: Express the following functions in the form u+iv • f(z) = \n (1+z) P

A: Given function is: f(z)=ln(1+z) Let z=x+iy

Q: Evaluate y' of the given functions: 1. y = (x² – 2)(x + 3)

A:

Q: Find the values of a and b that make the following function dif- ferentiable for all x-values. Jах +…

A: To be differentiable at x=-1  The function must be continuous at x=-1 So we plug x=-1 in both…

Q: 17. Find the linear function f(x) that is parallel to 4x + 3y = 6, such that f(0) = 7.

A: Given function, 4x+3y=6, That is 3y=-4x+6 y=-43x+2 compare to y=mx+c Therefore m=-43

Q: find all possible functions with the givenderivative.33. a. y′ = x b. y′ = x2 c. y′ = x3

A: a. Given, y'=x⇒dydx=x⇒dy=x dx Integrating on both sides, we get ⇒∫dy=∫x dx⇒y=x22+C            ∵∫xn…

Q: Form a PDE by eliminating the arbitrary function ø from $(x* + y² - z°.z? + 2xy)=0

A:

Q: Given f(x,y) = x²y-3xy³. Evaluate 2 S₁² 0 fdx

A: Follow the procedure given below.

Q: Find f'(1) given that f(x) ax+b cx+d' where a, b, c, d are constant.

A: we have to find derivative.

Q: Find the most general antiderivatives of each of the following function

A:

Q: Find the function F(x) such that F' (x) = 8x and F(0) = 1 O 1+4x^2 O 4x^2

A: topic- Functions

Q: Find the value of a, b, c and d if f(x) is differentiable (asinx – bcosx + x f(x) = x2 + 3 4 > x > 0…

A:

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: For f(x, y) = xex2y, find fx and fy, and evaluate each at the point (1, ln 2).

A: Given: fx,y=xex2y

Q: Find the value of c in the interval (a,b) such that f'(c)=0 for f(x)=(x-3)(x+1)´ on[[-1,3].

A: the value of c is:-

Q: Calculate L3, R3, and M3 for the following function over the interval [0,3]. f(x) = Vx + 1

A: The given function f(x)=x+1 over the interval [0,3]

Q: cx +5 f(x) = for x 2

A: Explanation of the answer is as follows

Q: Given f(x, y) = 4x°y+ 7xy*. Compute:

A:

Q: let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

A:

Q: Differentiate the function y = Inx• In 13x. y' =O

A:

Q: For what value of the constant c is the function f continuouson  (∞,-∞)?

A:

Q: Find f such that t'(x) = x - 2 and f(0) = 6. f(x) = O

A:

Q: Find Ay and f'(x)Ax for y = f(x) = 6x, x =4, and Ax = 0.06.

A:

Q: Find f'(x) of each of the following functions. 2x+1 (c) f(x)=, ²+3 3x-1 (d) f(x)=In 2x+1)

A: Explanation of the answer is as follows

Q: Evaluate y' of the given functions: 1. y = √(3x+4)(x+3) 2. xy2 = x2

A: 1. Given function is: y=3x+4x+3 Then we get, y=3x2+4x+9x+12⇒y=3x2+13x+12 Differentiating y with…

Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: Find a functionf and a number a such that f(t) -dt = 3x-1 t6 2 + f(x) = a =

A:

Q: Use the formula to express w as a function of t if w= s/s+6 and s=t2+7 w=?

A: given :ω = ss+6   .... *s = t2+7

Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =…

A: From the given function it can be observed that it is continuous for all values of x less than 5 and…

Q: Find a and b so that the function f(x) = S 4x – 7x² + 5, a -2 is both continuous and…

A:

Q: a) Consider the function f(x, y) = /In (4 – x² – y?). Find the domain and range of f(x, y).

A:

Q: B. For each of the following functions z, find az az a2z and дх? дудх" дхду ay2 1. z = 2x? – 5xy +…

A: We know that when we differentiate a function partially with respect to 'x' , other variables of…

Q: For the function h(x,y) = ?x = x +9y 2xy-9 ah əh find and ax ду

A: We need to find derivative.

Q: A/ Derive by definition: y = Vx - 3 ? B/ Determine the value of (z) and (k) that makes the function…

A:

Q: Find h'(x) given that h(x) = Vx² +1

A: To do this problem we need chain rule  Chain Rule (using ’ ) f'(g(x))= f’(g(x))  g’(x) We will use…

Q: Evaluate the function at the given values of the independent variables. = x³ + 3xy + y²; x = -1, y =…

A: z=x3+3xy+y2x=-1  and y=1 Replace the x  and y values in the given function

Q: This function f(z)=(x^3-3xy^2)+i(3x^2 y-y^3) is differentiable O True False

A: Given :f(z)=x3-3xy2+i3x2y-y3

Q: Suppose f(x, y) = xy² + 4. Compute the following values:

A:

Q: Use a formula to express y as a function of t if  y = 3x2 + 9x and x = t − 1.   y =

A: First of all, both equations i.e. y in terms of x and x in terms of t.

Q: Compute the following values for the given function. f(x, y) = 8xye(x2 + y2) f(0, 0) f(0, 1) f(1, 1)…

A:

Q: de fined as F(X) = P(X f(t) for – a <x < a. - t<a

A: Here f(t) is probability density function of x.  Where -a&lt;x&lt;a.

Q: the domain of the function : y = In(x² + x + 1) is [0,0) Select one: O True O False

A: From the given problem:   y=lnx2+x+1   We know that logax is defined when x,a&gt;0.

Q: Find Ay and f'(x)Ax. For y = f(x) = X = - 1.6, and Ax = 0.1

A:

Q: Find and for the functions: ax ду 1 f(x, y) = x Jy + y5 – :

A:

Q: se the variable u for the inside function to express each of the following a (a) y = 910x-1 O u =…

A: Topic = Functions u=10x-1 , y=9u

Q: dx (b): Evaluate the Jo (1+x)(2+x)/x(1-x)

A:

Q: Determine the following a) f(r² -x=1)dx

A:

Q: Evaluate the following functions at the given algebraic arguments. g(y) = 5y at y = x², y = 2x + 1,…

A:

Q: B- Obtain PDE by eliminating the arbitrary functions from the following; 1. z = xf1(x + t) + f2(x…

A: The partial derivative of the function z=f(x,y) is denoted as follows:…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.