171 Answered Questions for the topic calc

#### Calculus Problem

find y',y'(3) and the equation of the tangent line to the curve, x^2+(sin(2*pi*y)) = 9, at the point (3,8)1) the derivative of x is given by y'=.....2)the slope of the tangent line to the curve at...
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#### Matrix solve for b

I have a matrix of Ax=b. That is 3X4. With the entry x+3y+7z=12. 1x+4y+10z=15. And 2x+3y+5z=X or we can call X really b3. I believe I need to somehow reduce to row echelon and solve for b3 by...
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#### Help me with this integral problem?

Show whether ∫ 1/x^4 dx from -1 to 2 is convergent or divergent. If convergent, evaluate the integral. Here's my work:After integrating, I got [-1/(3x^3)] from -1 to 2 and I got -3/8 as the answer...
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09/26/19

#### Find the slope of the tangent line to the curve defined by x^6+6xy+4y^2=176 at the point (2,4).

This is a derivative but I don't know how to do this question! I would appreciate if all work is shown with detailed steps! Provide the answer to the slope of the curve at the point (2,4) is_____.

#### Simplifying for derivative

consider the function f(x) = 4sqrt(x)-1a) Simplify as much as possible in f(4+h)-f(4)/hb) Use the result to find the derivative of f'(4)

#### Alternative method for Derivatives

Let f(x) = 5/(x+3)A) . Reduce with the definition f(x)-f(1)/x-1 so that there is only one x.B) . Use that answer from a to find derivative f'(1)

#### Use interval notation to indicate where 𝑓(𝑥) is continuous.

Let f(x)= the cubed root of 3x-5Use interval notation to indicate where 𝑓(𝑥) is continuous.I found x to be 5/3 and the interval notation to be [5/3,INF) however it is saying it is incorrect and I...
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Calc Calculus

09/06/19

#### What value of a will make this continuous at x=0?

The function f is given by the formula f(x)=(2x)/x^2+6x when x<0and by f(x)=cos(x)+a when x>(or equal to)0What value must be chosen for a in order to make this function continuous at x=0?

Calc Calculus

08/18/19

#### TRUE OR FALSE: For all real x, y and z we have that |x − y + z| ≤ |x| + |y| + |z|

TRUE OR FALSE: For all real x, y and z we have that |x − y + z| ≤ |x| + |y| + |z|

Calc Calculus

08/18/19

#### True/False: Let b ∈ R, b>0 and let B:={x^2 | x ∈ (−b,0)}. We then have that inf(B) = 0 and sup(B) = b^2

Statement: "Let b ∈ R, b>0 and let B:={x^2 | x ∈ (−b,0)}. We then have that inf(B) = 0 and sup(B) = b^2"I'm not sure where to start with this question. Can anyone help?

Calc Calculus

07/05/19

#### lim n-->infinity 1^n

Is lim n −>infinity 1^n simply 1? I know 1^infinity is indeterminate form, but I read somewhere that you only have to apply log differentiation if it is a function raised to another function. If...
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Calc Calculus

06/30/19

#### Infinite series 7 / ( n^(1+(1/n)) ) from n = 8 to infinity. What test do I need to determine if this converges or diverges?

Infinite series 7 / ( n1+(1/n) ) from n = 8 to infinity. What test do I need to determine if this converges or diverges? Is ratio test involved or is another test needed? Please show work.

Calc Calculus

06/30/19

#### Infinite series 1/(2+3^n)

How do I prove the infinite series 1 / (2+3n) starting from n = 4 to infinity converges? I must use the ratio test but when I do so I am not getting a number less than 1.

Calc Calculus

06/29/19

#### Find the sum of the infinite series (-1 + (-3)^n) / 4^n from n =2 to infinity

Find the sum of the infinite series (-1 + (-3)n) / 4n starting from n = 2 all the way to infinity. I figured it would be a geometric series, but I am having trouble finding the ratio in order to...
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Calc Calculus

06/29/19

#### Infinite series (ln(n))^998/n^(7/8) diverges

Can someone please explain why the infinite series (ln(n))998/n(7/8) diverges and doesn't converge? I was looking at the relative growth rates and noticed that nq (with q being a number greater...
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Calc Calculus

06/26/19

#### Why is the infinite series n^n/(n+1)! and n^(n+1)/n! divergent by the ratio test?

Why is the infinite series nn/(n+1)! and n(n+1)/n! divergent by the ratio test? I see how it is divergent by the test for divergence, but I am supposed to prove it through the ratio test. Every...
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Calc Calculus

03/13/19

#### A kite 100 ft above the ground moves horizontally at a speed of 12 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of st

A kite 100 ft above the ground moves horizontally at a speed of 12 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let...
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Calc Calculus

01/19/19

#### limx-->1^+ ((x^2+5x-6)/(|x-x^2|)

limx-->1+(x2+5x-6)/(|x-x2|)The correct answer is 7 but I keep getting -7. I think I am doing something wrong with the absolute value bars. Can someone please show the steps for this?

Calc Calculus

01/19/19

#### f(x) = 1/(x^3-1) 1) lim x--> 1^- f(x) = 2) lim x--> 1^+ f(x) =

f(x) = 1/((x3-1) 1) lim x--> 1- f(x) = 2) lim x--> 1+ f(x) =I would like to understand the steps on how to answer these questions.

Calc Calculus

01/19/19

#### limx-->pi/2^+ (-8/cosx)

limx-->pi/2 (-8/cosx)evaluate the right hand limitI keep getting -8/0+ (since cos(pi/2) is approaching zero from the right hand side) and keep getting negative infinity as my answer, but correct...
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Calc Calculus

01/13/19

#### f(x) = x^2 - 12x, x<=6 (x is less than or equal to 6). Find the inverse of f(x).

f(x) = x2 - 12x, x≤6. Find the inverse of f(x). I was told to use the quadratic equation, but when I do that I get a numerical answer and not an inverse equation.

01/12/19

#### Find f^-1(4) of f(x) = x^9 + x^3 + x + 1

Find f-1(4) of f(x) = x9 + x3 + x + 1The only way I know how to do this is by using a graphing calculator. I don't know how to solve it by hand though. If anyone knows what I should do, please let...
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12/09/18

#### Calculus (derivatives)

Calculus derivative helphttps://docs.google.com/document/d/1UfT3mFkkl48xP202eFL9o0CRVIq_YedMSSRpH5ztvX0/edit?usp=sharing(It wont let me add images so everything is in this google doc!)

Calc Calculus

12/03/18

#### Consider the function

f(x, y) = x2 + xy + y2 defined on the unit disc, namely, D = {(x, y)| x2 + y2 ≤ 1}. Use the method of Lagrange multipliers to locate the maximum and minimum points for f on the unit circle. Use...
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