4 (3) Find the equation of the line tangent to f(x) = 2x – 2x2 +1 at x = 1. [Hint: f'(a) is the slope of the line drawn to the curve at the point (4) Find the values of a and b so that h(x) is continuous at x = 4. Hint: Write down the limit definition of continuity -xa + 26 { 4b for x < 4 h(x)3= for x = 4 for x> 4

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

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A:

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A:

Q: The function y = 1/x does not take on either a maximum or a minimum on the interval 0 &lt; x &lt; 1…

A: Extreme Value Theorem:If a function f(x) is continuous on a closed interval [a,b], then f(x) has…

Q: Given the piecewise function f(x) = = Why is f not differentiable at x = 4? Of has no tangent line…

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

Q: 32? And are

A: {x2                               if x&lt;-2f(x)={x1/5                           if…

Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

A:

Q: Find the equation of the tangent line of f(x) = sqrt(x+1) at x = 0 using the definition of limits.

A: To find: The equation of tangent of line. Given: The function is f(x)=x+1. Concept used: Slope…

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A: To obtain the value of limx→03x-fx4x-fx, substitute 0 for x and 1 for f(0) in the expression, and…

Q: Express the limit as a definite integral. 4 lim non + (i/n)- (i/n)9

A:

Q: (a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

A:

Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

A:

Q: 1-cos 2x lim X→0 x2

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

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A: Given

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A: NOTE: Refresh your page if you can't see any equations. .

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A:

Q: 1. To take the derivative of the following function. х т (1) y = m (2) y = x' log 2. To find out the…

A:

Q: Which of following limits is the derivative of g(x) =5x at =2? 10 – 5h lim h 10 + 5h lim h>0 h 10 +…

A:

Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

A: This question is taken from the limit in which we have to check the continuity at x=0 of the given…

Q: Express the limit as a definite integral on the giveninterval.

A:

Q: Express the limit as a definite integral on the given interval. lim -Ax, [1, 3] (x†)² + 2 i = 1 dx

A:

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

A:

Q: Given f(x) = |2x – 2|. 1) At which points is f not differentiable? Prove your claim using the limit…

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Q: Show that the limit of the function does not exist xy lim (xy)-(0,0) x2 + y?

A: We have to show that limit of the function does not exist.

Q: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

A:

Q: Find the limit as x approaches infinity of f(x) when f(x) is x times square root of x

A: x times sqrt(x)= x times x^(1/2)= x^[1+1/2] = x^(3/2)

Q: (B) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D

A: Explanation of the answer is as follows

Q: let f(x)= 5x2. Show that f(3+h)=5h2+30h+45. Then show that  (f(3+h)-f(3))/h=5h+30 and compute the…

A: Compute: f(3+h)

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A:

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A:

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Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x-0 sin4x 2- lim…

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Q: Use a derivative (not L'Hospital's Rule) to evaluate (2 + h)4 – 16 lim h Enter the limit in the…

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Q: a)Express the limit as a definite integral. Σ (3c-5)Ax, xe[0,1] lim 2 b) and then evaluate it.

A: lim∆→0∑i=1n3c2i-5∆xi  x∈[0,1]∑ =∫∆xi=dx∫01(3x2-5)dxThis is definite integral

Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

A:

Q: Express the limit as a definite integral on the given interval. lim S 19(x/)³ – 8x;]Ax, [2, 5] 1

A: The definition of definite integral is, ∫abf(x) dx = limn→∞ ∑i=1n f(xi*)△x   in the interval a, b…

Q: 21. Discuss the continuity of : 1 x+ - for x 2 (ans.: discontinuous at x-0,2 ; continuous at x-1)

A: We have to check for the end points.

Q: Find the limit as x approaches zero of f(x)=tan(x)/x

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: The given question is related with limits. Given that fx , y = 3y9x2 + 4y2 . We have to find two…

Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

A:

Q: Find the limit as x approaches negative infinity of (xe1/x-x)

A:

Q: 1. Find the points at which f is discontinuous. At each of these points, state the type of…

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Q: 1 . Let f(r) 2r + 1

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Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(7x) lim x →0

A: Given:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.