Let f(z) = 2z? – 3–ze" +e**. Describe this function in detail.

Q: Let y=sin2x. Differentiate this function without using the chain rule.

A:

Q: Use mathematical induction to prove that the derivative of f (x) = xn equals nxn−1 whenever n is a…

A:

Q: 75. F(x) : (t + 2) dt

A:

Q: Find the derivative of the function by the limit process. f(x) = x2 - 2 %3D f'(x) = 2x %3D Need…

A: Apply Limit rule

Q: Show that the function is continuous. f(x) = x sinx

A:

Q: find I of implicit function sec""cImcy)- In(8**) when yoo

A: 9999

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

A:

Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: Compute the derivative of f (x) = x3/2 using the limit definition. Hint: Show that

A: we have;  f(x)=x32

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

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Q: Let f(x) = sinh(2x) then f'(In2) = %3D %3D

A:

Q: Find f'(a) using the definition of the derivative. if f(x) = Use the definition of %3D derivate…

A:

Q: Find where the function is continuous, but not differentiable..

A: Given,

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

A:

Q: 4. Is the function f integrable over the interval [-4,1]? Briefly justify your answer. 2x2 + 5x – 3…

A: Solution  Question 4  Given,  fx = 2x2+5x-3x+3  We have to find the function is integrable in the…

Q: Compute the derivative of f() = arcsin(x² e3x). %3D

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

A:

Q: 7. Differentiate the function using quotient rule. хех y = x + ex

A:

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Define wronskian of Two Functions?

A: Wronskian of two function: Let f(x) and g(x) be two differentiable functions, then wronskian of f(x)…

Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = - %3D 5+x? (Use decimal…

A: fx=115+x2,a=2;∆x=-12 Now, differentiate the function with respect to x.…

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

A:

Q: Assume that f is a function with domain [0,1] that is differentiable in (0,1). Assuming that f (0) =…

A:

Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Find four relations from {a, b} to {x, y} that are not functions from {a, b} to {x, y}.

A: It is given that the two sets are {a, b} and {x, y}. It is known that if A and B are the sets then…

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

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Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

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Q: Find all values of a and b that make -а - х, x<-2 f(x) = {bx? + 1, Vx+b, -2<x<1 x21 continuous…

A: The function is given by: f(x)= -a-x , x&lt;-2           bx2+1 , -2≤x&lt;1         x+b   , x≥1 Also…

Q: Find continuous functions

A: Given,        fn:0, 1→[0, ∞)

Q: 1, cosX, cos 2X,--- , cos mx

A:

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: find the value of c that make the function continuous

A:

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Use the ħndanental Theorem Ot calculus part I to find the derivative Of hx)=

A:

Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Vx + y + 1 f(x, y) ,æ In (y² – x) х — 1 -

A: Given: fx,y=x+y+1x-1,xlny2-x A function f(x,y)=Mx,y,Nx,y is said to be continuous on the points…

Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

A:

Q: Give an example of a function that is integrable on the interval [−1, 1] but not continuous on [−1,…

A: Let fx=x       Greatest integer function. Now, ∫-11x dx=∫-10x dx+∫01x dx=∫-10-1 dx+∫010…

Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

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Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

A:

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.