promath The derivative of cos3x is equal to -3sin3x. Here we learn how to differentiate cos3x and find the derivative of cos3x by first principle. Derivative Formula of cos3x The formula of the derivative of cos3x is given by d(cos3x)/dx = -3sin3x. That is, the derivative of cos3x is equal to the negative of three times … Read more
The integral of sinxcosx is equal to -(cos2x)/4+C or, (sin2x)/2+C where C is an integration constant. In this post, we will learn how to integrate sinx cosx. The integration formula of sinxcosx is give as follows: Find the integration of sinx cosx Answer: The integration of sinx cosx is (sin2x)/2+C. proof: There are three methods … Read more
The limit of sin2x/sin3x when x approaches 0 is equal to 2/3, that is, limx→0 sin2x/sin3x = 2/3. The limit of sin3x/sin2x when x approaches 0 is equal to 3/2, that is, limx→0 sin3x/sin2x = 3/2. The following formula will be useful to compute the above limits: limx→0 sinx/x = 1 …(∗) Limit of sin2x/sin3x … Read more
The limit of sin2x/x when x→0 is equal to 2 and the limit of sin2x/x when x→∞ is equal to 0. Here we find the limits of sin2x/x when x tends to 0 or ∞. The formulas of the limits of sin2x/x when x→0 or x→∞ is given below: Find limx→0 sin2x/x Answer: The function … Read more
The limit of sin(1/x) as x approaches 0 does not exist, that is, limx→0 sin(1/x) is undefined. The limit formula of sin(1/x) when x→0 is given below: limx→0 sin(1/x) = undefined. Let us learn how to find the limit of sin(1/x) when x approaches 0. Find the Limit of sin(1/x) when x→0 Answer: The function sin(1/x) has no … Read more
The limit of tanx/x as x approaches infinity does not exist, that is, limx→∞ tanx/x is undefined. Here we learn to find the limit of tanx/x when x tends to infinity. The formula of the limit of tanx/x when x approaches ∞ is given by limx→∞ tanx/x = undefined. Below theorem will be useful to prove this … Read more
The limit of tanx/x as x approaches 0 is equal to 1, that is, limx→0 tanx/x = 1. Here we learn to find the limit of x/tanx when x tends 0. The formula of the limit of tanx/x when x→0 is given by limx→0 tanx/x = 1. Proof of limit tanx/x = 1 when x→0 First, we prove … Read more
The value of the limit of x/cosx is equal to 0 when x approaches to 0. Here we will learn how to find the limit of x/cosx when x tends 0. The formula of x/cosx limit as x goes to 0 is given below: limx→0 $\dfrac{x}{\cos x}$ = 0. Proof of limit x/cosx is 0 when … Read more
The general solution of dy/dx=ex+y is equal to ex+ e-y= C, and the solution of dy/dx=ex-y is given by ex – ey= C. Here C denotes an arbitrary constant. Let us learn to solve dy/dx = e^(x+y) and dy/dx = e^(x-y), and find their general solutions. General Solution of dy/dx=ex+y Answer: The general solution of … Read more
The general solution of the differential equation dy/dx=sin(x+y) is given by tan(x+y) – sec(x+y) = x +C where C is an arbitrary constant. Here we will learn how to find the solution of dy/dx=sin(x+y). Let us now solve the differential equation dy/dx=sin(x+y) by the substitution method. General Solution of dy/dx=sin(x+y) Question: Find the general solution … Read more